"And", "but", "of", "the", "is/are" are included in the meaning as mere connector words. Other additions are bracketed.

Notes and Possible Meanings

(The notes concentrate on the more difficult meanings. 
The names Lord and Jah and Jehovah are used interchangeably.)

--- but I will make Babylon sink down and fade away! ---

This is a key name, and nearly all the possible meanings fit well and have been included. While there are several different possibilities, there is increasing agreement among scholars that the name refers to Babylon in some way. This line of names that reads, "The fame and/of the stronghold/boundary of Babylon extends beyond the border/divide," ends with Peleg and this is also where the genealogy branches out into the period of the tower of Babel. Babel is also where they sought to make a "name" (fame) for themselves. Therefore, perhaps the "stronghold of Babylon," is just another name for the "tower of Babel" in Babylon.

(Or may read, "I will make Babylon sink down/fade away!") I believe both are intended as a play on words, and this is reflected in the code.

Gospel of Luke (ch. 3:36) follows the LXX version that adds the name Cainan between Arphaxad and Shelah. Though almost certainly a textual error in the LXX (a repeating of #4), yet because Luke used it so have we. However, the names code can read fine without it.

Israel

A mighty one struggles (in prayer)! 

A righteous Prince sees God!

Jacob: "He holds back"; "he takes the heel"; "One who follows on another's heels" figuratively meaning, "A deceiver"; "He will deceive". In the context of the bible in keeping with the context of this code it seems to mean, "he outwits", or, "he outmaneuvers". The name may also mean, "He will recompense"; "He will reward"; "He will keep guard over"; "He will protect". (Jacob is likely a shortened form of, Jacobel (יעקבאל), meaning, "God will reward/recompense"; "God will keep guard over". ISBE.)

Jacob had his name changed to Israel. However, like Jacob, the name can means several things, and the bible appears to use each meaning. Israel can mean "One who wrestles with God", "God/Mighty-one will fight"; "Let God contend"; "God prevails"; or, "A prince with God". "God will rule as a prince"; "He will rule as God". (The key Hebrew word here, sara, can mean both a 'prince' or "to fight". Compare Jacob/Israel to Abraham's wife. She had her name changed from Sari, meaning "to struggle/fight," to Sarah, meaning, "Princess", Gen. 17:15.) Also it may be related to or sounds like, "A man sees God". {From איש ish, a man, (the א aleph being dropped), and ראה raah, he saw, אל el, God. (Clark's Commentary.) Moreover, this agrees with what Jacob said at the place he wrestled, "I have seen God..." Gen. 32:30.}

It is interesting that the names' Jacob and Israel are applied to the Lord in the code because the same is implied in Gen. 32:29 when Jacob asks what the Lord's name, the One who was "wrestling/fighting" with him. The name(s) given to Jacob are really God's own name(s)! (See Ps. 18:26, "With the pure Thou showest Thyself pure, And with the perverse showest Thyself a wrestler", YLT.)

Gen. 32:25-27 "And when he saw that he prevailed not against him, he touched the hollow of his thigh; and the hollow of Jacob's thigh was out of joint, as he wrestled with him. And he said, Let me go, for the day breaketh. And he said, I will not let thee go, except thou bless me. And he said unto him, What [is] thy name? And he said, Jacob." Gen. 32:28-30 "And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed. And Jacob asked [him], and said, Tell [me], I pray thee, thy name. And he said, Wherefore [is] it [that] thou dost ask after my name? And he blessed him there. And Jacob called the name of the place Peniel: for I have seen God face to face, and my life is preserved." (Also see Hosea 12:3-4, "Jacob took his brother by the heel in the womb, and by his strength he had power with God: Yea, he had power over the angel, and prevailed: he wept, and made supplication unto him: he found him [in] Bethel, and there he spake with us".) The code picks up again on the theme of intercession in #48. 

"Israel" also sounds like, "The upright one". This too is reflected in the code. The bible alludes to what the name Israel sounds like, "Isharel", meaning, "God is righteous", in Num 23:10, "Who can count the dust of Jacob, and the number of the fourth [part] of Israel? Let me die the death of the righteous, and let my last end be like his!" The nation "Israel" is even given the honorary name of Jeshurun (Dt. 32:15; 33:5,26; Isa. 44:2), meaning, "the upright one". The International Standard Bible Encyclopedia (ISBE) says, "Most moderns take it as a poetical or ideal title of Israel, derived from ישׁר, yāshār, “upright”; it is held to contain a tacit reference to the word Israel (ישׁראל, yisrā'ēl), of which the first three consonants are almost the same as those of “Jeshurun”'".

Gen. 29:35, "And she conceived again, and bare a son: and she said, Now will I praise the LORD: therefore she called his name Judah; and left bearing."

Compare this portion of the code, "Praise (Judah) breaks forth and opens a way into a place that is surrounded by a high wall where the people of the prince are safe from the false prophet, being clothed with strength", with Num. 10:14, where the tribe of Judah leads the way from Mt. Sinai ahead of all Israel with the wall of fire by night, led by Moses the righteous prince. Therefore, Moses is the "mighty one" who "intercedes" and "sees God" at Sinai in #22, as did Jacob/Israel at Peniel, and who "outwitted his enemy" (#20-22), Pharaoh, at the Red Sea. There, God and all Israel rejoiced and laughed and mocked their enemies in song and dance --- Pharaoh and the false prophets (#28) (magicians) disgraced, along with the false prophet, Balaam, 40 years later. 

Balaam himself prophesied (contrary to his will) and said, Num 23:21-23 "He hath not beheld iniquity in Jacob; Neither hath he seen perverseness in Israel: Jehovah his God is with him, And the shout of a king is among them. God bringeth them forth out of Egypt; He hath as it were the strength of the wild-ox. Surely there is no enchantment with Jacob; Neither is there any divination with Israel..." (Also see note for #25 and #28.)

But both verb and noun used in Gen. 38:29 in reference to Perez birth, and so it has been used in the code in the exact same manner, (Gen. 38:28-29), "And it came to pass when she travailed, that the one put out his hand; and the midwife took and bound upon his hand a scarlet thread, saying, This came out first. And it came to pass as he drew back his hand, that behold, his brother came out; and she said, How hast thou broken forth? this breach (opening) be upon thee: therefore his name was called Pharez. (Perez)" (Webster) (Compare with 2Sam. 6:8.) (See next notes.)

Perhaps alluding to the pillar of fire that protected the Israelites, and to the "wall of water" at the Red Sea crossing, and ultimately to the New Jerusalem "having a wall great and high", (Rev. 21:12).

Ex. 14:21-22, "And Moses stretched out his hand over the sea; and Jehovah caused the sea to go back by a strong east wind all the night, and made the sea dry land, and the waters were divided. And the children of Israel went into the midst of the sea upon the dry ground: and the waters were a wall unto them on their right hand, and on their left." Ex. 15:8, "And with the blast of thy nostrils the waters were piled up, The floods stood upright as a heap; The deeps were congealed in the heart of the sea." (For "blast of nostrils" see #18-19.)

Rev. 21:10-13, "And he carried me away in the Spirit to a mountain great and high, and showed me the holy city Jerusalem, coming down out of heaven from God, having the glory of God: her light was like unto a stone most precious, as it were a jasper stone, clear as crystal: having a wall great and high; having twelve gates, and at the gates twelve angels; and names written thereon, which are the names of the twelve tribes of the children of Israel: on the east were three gates; and on the north three gates; and on the south three gates; and on the west three gates."

Note that the main opening/"gate" in the "high wall" is Judah, as implied by the position of the 12 tribes around the ark of the covenant in the day of Moses when they camped, (i.e., Judah/"praise" would be the main middle gate facing east.) Note, "the glory of God coming down from heaven"

Amminadab was a prince of the tribe of Judah (Num. 7:12) who lived at the time of Moses and likely saw the Exodus. Perhaps the word "Prince" in the code is meant to remind us of Moses who was called a Prince, and thus the high wall of #25-26 perhaps alludes to the pillar of fire that led Israel in the desert.

Nahshon's sister was Aaron's wife, (Ex. 6:23). Nahshon is called, "The Prince of the people of Judah," because he led the "the camp of Judah" during the wilderness wanderings (Num 1:7; 2:3; 1Chron. 2:10-12; Matt.1). He would have been alive at or just before the time of Balaam the false prophet. Nahshon would have died in the wilderness under a curse along with all that "generation", (Num. 14). Because the only thing the bible has to say about Nahshon is that he was "the leader of the people of Judah" during the wilderness wanderings, I believe that he is both a type of the beast (antichrist) as a "leader", and of the "false prophet" (as per the meaning of his name). Both are here symbolized in this one man. The bible does not say that Nahshon was himself a bad man, but it appears that God is using the fact that prince Nahshon led a doomed people in the desert to become a type of the antichrist/false prophet to come who will do likewise. Moreover, the theme of the wilderness wonderings is prominent in the book of Revelation where the beast and the false prophet are discussed, (Rev. 12-13). (Compare Rev. 12:6,14 with 17:3. Note the contrast of the faithful with the unfaithful "woman" "in the wilderness".) Also note the contrast with the prior name; "The people of the Prince" (likened unto Moses) "are safe from the (false prince) and Prophet." Moreover, the Two Witnesses of Rev. 11 are comparable to Moses and Aaron (or Elijah) in the book of Revelation in that Aaron was Moses' prophet/representative just as the "Beast" (antichrist) of Revelation has the "False Prophet" as his own prophet/representative. Thus, it seems more than coincidence the the sister of Nahshon was Aaron's wife! (Ex. 6:23). (Also see note for #23.)

Positively speaking, Nahshon sounds like and is related to the word for "Nehushtan", and Num. 2:3 about Nahshon as "The Prince of the people of Judah," --- the word "Prince" literally means, "to be lifted up"; and, Nehushtan is the name for the 'snake on the pole' that was "lifted up" in the wilderness for the healing of the people of which Nahshon himself would have witnessed. Perhaps, then, Nahshon is also a type of Jesus lifted up on the cross (John 3:14) in the sense of the snake upon the pole? I believe Nahshon can therefore be viewed positively and negatively --- as Christ on antichrist --- but since the literal meaning of the name itself lends best to the latter, this is what I have put in the names code. (2Kings 18:4 "He removed the high places, and brake the images, and cut down the groves, and brake in pieces the brazen serpent that Moses had made: for unto those days the children of Israel did burn incense to it: and he called it Nehushtan.") Thus the names would read: "The people of the Prince of the Snake on the Pole are safe..." Also note Rev. 22:14-15.

A Servant,

This name marks the middle of the 60 names and it also marks a subtle shift in who is speaking --- apparently, (as I interpret it), moving from God the Father to now God the Son. The name Obed ("servant/serving") applies equally well to both the previous thought and to the next thought, and I have gone with the latter. However, one can choose either or without significantly altering the flow of thought. It is perhaps significant that of the 6 days of creation, the first 3 were days of forming and the next 3 were days of filling what was formed. This seems to be the pattern of the 30 + 30 names here. If so then #1-4 is in parallel to #31-35.

(Or, I exist as...)

Some Greek manuscripts in Matthew have Asaph for Asa (although Asa is clearly meant). Sometimes a name can end up altered somewhat in ancient times. Asaph means "one who gathers". If it is used instead then the Names-Code reads, "My Father, the Lord, will gather (to himself) him whom He (lit. "Lord") judged and raised up." ("To gather" is an Hebraic expression {Gen. 25:8,17}meaning, "To gather one to their fathers upon death". Here, Jesus is "gathered" to His father?)

Ahaziah - “Yah holds, or sustains”; "Held by Jehovah"; “Jehovah (Yahu) holds (possesses)”; "Jah has seized".

2Kings 14:21 - Uzziah is also called Azariah, 2Chron. 26:1. The former signifies, "My strength is the Lord"; the latter, "The help of the Lord". Our rendering is a compilation of both.

“Jehovah has helped”; "Whom Jehovah helps."

"Jehoiachin (je-hoi´a-kin) (יהויכין, y^{ehōyākhı̄n, “Yahweh will uphold”; called also “Jeconiah” in 1Ch_3:16; Jer_24:1; יכניה, yekhonyāh, “Yahweh will be steadfast,” and “Coniah” in Jer_22:24, Jer_22:28; כּניהוּ, konyāhū, “Yahweh has upheld him”; Ἰωακείμ, Iōakeı́m): A king of Judah; son and successor of Jehoiakim; reigned three months and surrendered to Nebuchadnezzar; was carried to Babylon, where, after being there 37 years a prisoner, he died." Coniah "The Lord did uphold."}

Since this king had three similar names, I have taken the three main meanings and combined them. The context determines tense because tense can be blurred in Hebrew when dealing with prophecy, with the exception of Jeconiah. He had three names basically the same, two of which were exactly the same except for one being future and the other being past tense. Therefore, since the names themselves make this distinction, it is thus reflected in the code. 
(Compare #45-47 with #36-39.)

The insertion of Pedaiah is questionable. It is not included in Matthew, but neither are a few other names. (The following is quoted from John Gill's "Exposition of the Entire Bible") on 1Chron. 3:19-24 -  "And the sons of Pedaiah were, Zerubbabel and Shimei,.... Here arises a difficulty, since elsewhere Zerubbabel is said to be the son of Shealtiel, (Hag. 1:1) some think this is not the same Zerubbabel here as there; so Grotius (u); but I see no reason for that; but this difficulty may be removed by observing, that if Pedaiah was a son of Salathiel (Shealtiel), as Kimchi thinks, then Zerubbabel, being his grandson, may be called his son, as grandsons are sometimes called sons in Scripture; or rather, Salathiel, having no children, adopted Zerubbabel, his brother's son, and made him successor in the government; so that he was the son of Pedaiah by birth, and of Salathiel by adoption; or else Salathiel dying without children, his brother Pedaiah, according to the law, married his widow, and by her had Zerubbabel, who was the proper son of Pedaiah, and the legal son of Salathiel:"

Joseph, the father (not by birth) of Jesus was likely named after Joseph the son of the patriarch Jacob, and thus Gen 30:24 is relevant, "And she called his name Joseph; and said, The LORD shall add to me another son."

Isa. 9:6-7 "For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace. Of the increase of [his] government and peace [there shall be] no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the LORD of hosts will perform this."

Also named, "Emmanuel", meaning, "God is with us"; and "Christ", meaning, "Messiah".