I do not know whence either the Matthean or the Lucan genealogies derived the names after those which appear on the pages of scripture, but my overall take on the Lucan genealogy is inspired mainly by Richard Bauckham.
The Lucan genealogy lists 77 human generations from Adam to Jesus, counting inclusively; that is, Adam is the first generation and Jesus is the seventy-seventh. Certain important people in Jewish history appear as the last generation within their own group of seven. For example, Enoch rounds out the first seven, Abraham the third, David the fifth, and Jesus the eleventh. Furthermore, another man named Jesus rounds out the seventh seven, in position 49, a jubilee figure. Thus Enoch is the seventh human generation ("seventh from Adam," according to Jude [1.]14), his son Methuselah the eighth. The genealogy, therefore, lists 70 human generations from Methuselah to Jesus, counting inclusively; that is, if we count Methuselah as the first generation after Enoch, Jesus is the seventieth.
The naming of Enoch in the seventh generation and of Jesus exactly seventy generations after him is probably no accident. The book of Enoch, also known as 1 Enoch, tells of the angels called the Watchers who had relations with human women, as per Genesis 6.1-4, and were thus condemned to be bound in the valleys of the earth until the great day of judgment, a total of seventy generations.
When were the Watchers bound? The Enochic literature is not entirely precise on that point, but on page 320 of
Jude and the Relatives of Jesus in the Early Church Richard Bauckham observes that "it certainly happened after Enoch's translation and during the lifetime of his son Methuselah. So a reader might easily suppose that it should be dated in the generation after Enoch's." The book of Enoch is divided into 5 sections, of which sections 1 and 3-5 are attested at Qumran; section 2, the parables, is not attested before Christian times. Methuselah does not appear in section 1 (or 2, for that matter), but each of sections 3-5 is set up as a direct address from the translated Enoch to his son Methuselah. Indeed, what Enoch is sharing with his son is vital information for posterity, for the generations of the world (82.1; 83.10).
We are probably justified, then, in seeing a connection, at least in hindsight, between these instructions to Methuselah for the generations and the seventy generations during which the Watchers are bound:
1 Enoch 10.11-14: 11 "And the Lord said unto Michael: Go and bind Semjaza and the rest with him who have had intercourse with women so as to have been defiled with them in their uncleanness. 12 And, when their sons have slain each other and they have seen the destruction of their loved ones, also bind them for seventy generations in the valleys of the earth, until the day of their judgment and consummation, till the judgment of the age of the ages is fulfilled. 13 At that time they shall be led off into the chaos of fire and into the torment and into prison to be shut up for the age. 14 And whoever shall be burned and ruined will from now be bound together with them until the end of generations."
Thus, although the immediate context of this passage includes instructions to Noah, the son of Lamech (10.1), it is easy to see how one familiar with the Enochic literature might start counting the seventy generations with Methuselah as the first. (This is especially true given that, according to all three extant versions of the genealogies in Genesis 5.1-32, Masoretic, LXX, and Samaritan, the lifespans of Methuselah, Lamech, and Noah overlap to a great degree.) If Methuselah is the one receiving instructions for all the generations, then it makes sense that all the generations (the seventy) should start being counted with him. Whether or not this is how the original author(s) of the Enochic literature intended the generations to be counted, what matters for our purposes is that this is a valid and plausible reading on the part of a Jewish reader from century I.
It seems, at any rate, quite a coincidence that (A) an ancient book written as instruction from Enoch to his son Methuselah should number the generations of the world at 70 and (B) a genealogy for the messiah, supposed to appear at the climax of history, should place that messiah in generation 70 after Enoch. I think, rather, that this is no coincidence at all. It is intentional.
It also helps explain the presence of Admin in the Lucan genealogy (Luke 3.33). In Ruth 4.19 and 1 Chronicles 2.9-10 Ram is the father of Amminadab; in Luke 3.33 Arni must correspond to Ram (Aram in Matthew 1.4), since both are said to be the son of Hezron, but his son is Admin, whose son is then Amminadab. No matter how the extra name Arni got onto the list, it serves a vital purpose to the christology of the genealogy, pushing David into the climactic seventh slot of the fifth septad. Without Arni, the genealogy would come out one name short of making David the seventh in his septad; possibly of related interest, in 1 Chronicles 2.15 David is named as the seventh son of Jesse.
I think Bauckham is most likely correct that the Lucan genealogy is basically an Enochic exercise.
ETA: In descending order (the reverse of how Luke actually presents it):
- Adam
- Seth
- Enos
- Cainan
- Mahalaleel
- Jared
- Enoch
- Methuselah
- Lamech
- Noah
- Shem
- Arphaxad
- Cainan
- Shelah
- Eber
- Peleg
- Reu
- Serug
- Nahor
- Terah
- Abraham
- Isaac
- Jacob
- Judah
- Perez
- Hezron
- Arni
- Admin
- Amminadab
- Nahshon
- Sala
- Boaz
- Obed
- Jesse
- David
- Nathan
- Mattatha
- Menna
- Melea
- Eliakim
- Jonam
- Joseph
- Judah
- Simeon
- Levi
- Matthat
- Jorim
- Eliezar
- Er
- Joshua
- Elmadam
- Cosam
- Addi
- Melchi
- Neri
- Shealtiel
- Zerubbabel
- Rhesa
- Joanan
- Joda
- Josech
- Semein
- Mattathias
- Maath
- Naggai
- Esli
- Nahum
- Amos
- Mattathias
- Joseph
- Jannai
- Melchi
- Levi
- Matthat
- Heli
- Joseph
- Jesus