There are references to the Name traditions in the New Testament. Perhaps the most famous is Philippians 2: 9:
'Therefore God also highly exalted him [Jesus] and gave him the name that is above every name ...' To a Jew such as Paul, this was clearly Yahweh. There is a strong argument that this passage of Philippians is a pre-existing hymn or song of praise which Paul is quoting, but in any case, it shows that both Paul and early Christians knew of the Jewish traditions of the Name and also, more shockingly for Jews, applied it to Jesus.
There are some very long and boring arguments in the scholarship about the titles applied to Jesus in the New Testament. He is frequently called 'Kurios', which translates the Hebrew 'Adonai'. Kurios is the word generally used to render the Tetragrammaton in the Septuagint, and Adonai is how it was pronouced in Hebrew when the Bible was read out (most people think) and I think most people consider that the early Christians knew what they were doing when they applied it to Jesus: they were assigning him a divine title. Some argue that, as with the English words 'Lord' or 'Sir', their use is simply a mark of respect. But I think that this is a weak argument, since many of the references are steeped in an Old Testament background, notably from the Psalms. Psalm 110:1 ('The Lord [Yahweh, translated as kurios] said to my Lord [Adonai, translated as kurios], sit at my right hand, until I make your enemies your footstool') is, I think I'm right in saying, the most frequently quoted OT passage in the New Testament. Cf Matthew 22: 43-45 for one instance. In all of these, it's clear that Jesus is being referred to with one of the names of God. And these are names that were at least sometimes euphemisms for the Tetragrammaton. I don't think any Biblical scholar would agree that the New Testament writers didn't know the traditions about the Tetragrammaton; I've certainly never heard that argument.
I also don't think it's really possible to argue that the New Testament isn't deeply Jewish. See the recent Jewish Annotated New Testament for details of just how Jewish beliefs and culture run through the whole thing. I think I've already mentioned just how 'Semitic' a lot of the Greek is (particularly Mark); it's less fashionable these days than it used to be to posit an Aramaic original underlying the Gospels, but it certainly seems that their writers were used to Hebrew and Aramaic texts (such as the Septuagint) and used those languages themselves. Paul says he is a Jew, a Pharisee, and he really must have been to know all the stuff he knows and think the way he thinks (for instance, on purity and pollution, a deeply Jewish way of thinking). As I also said upthread, that the New Testament is deeply Jewish doesn't mean it isn't also Greek, since Hellenism was so pervasive, even in Palestine, at this period. There's no neat boundary between the two.
I wanted to address this too, because I feel that the "Jewishness" of the NT Greek is usually grossly overstated. Words are taken to mean some Hebrew or Aramaic connection often for no reason than that you could translate them to Hebrew or Aramaic too, or that you'd use them to translate some Aramaic word. Which is is bogus enough to kinda start to irk me.
Point in case: Kurios.
Well, Kurios in Greek meant "lord", although probably more exactly, "master" or "owner". As in master vs slave. Someone who either literally owns you, or has enough rights over you that he might as well own you. A subcase being "guardian" (which at the time was much more of a master than you're nowadays to your kids.)
It comes from "kuros", meaning pretty much "supremacy." So "kurios" is one who has such supremacy over another or over some inanimate thing.
The word can be applied to a noble or king (e.g., the Roman Emperor would be called "kurios" by the Greeks, as Josephus tells us) but it could mean as little as one's father or legal guardian. or to the guy who owns something. E.g., for an unmarried woman, her father or if orphan her brother would be her "kurios". E.g., for some plot of land, the owner was a "kurios".
It's not just some wild guess by those pesky mythicists, it's what the word actually MEANT.
Even in the NT, it's used often enough for someone who is not God. Again, it's not some rationalization by those denying some imaginary Jewishness of the text, it's what the text actually says. E.g.,Matthew 25:18-21:
"But the man who had received the one talent went off, dug a hole in the ground and hid his master's money. After a long time the master of those servants returned and settled accounts with them. The man who had received the five talents brought the other five. ‘Master,’ he said, ‘you entrusted me with five talents. See, I have gained five more.’ His master replied, ‘Well done, good and faithful servant! You have been faithful with a few things; I will put you in charge of many things. Come and share your master’s happiness!’ "
All those highlighted words are "kurios". I could quote the rest of the parable, which has half a dozen more "kurios", but you can check it out for yourself if you want to.
Or John 13:15:
I tell you the truth, no servant is greater than his master, nor is a messenger greater than the one who sent him.
Again, we have a use of "kurios" for something very different than God.
Or to illustrate how it worked for inanimate things too, and simple ownership, here's what Matthew 20:8 says:
"When evening came, the owner of the vineyard said to his foreman, 'Call the workers and pay them their wages, beginning with the last ones hired and going on to the first.'
It may not be obvious in English, but that's the "kurios" of the vineyard in the Greek text. Go figure. (Incidentally Mark too uses the same "kurios" of the vineyard construct in his own story.)
Paul himself, although he does use "Lord" predominantly for Jesus, in Galatians 4:1 pulls a:
What I am saying is that as long as the heir is a child, he is no different from a slave, although he's the owner of the whole estate.
Yep, that "owner" is a "kurios".
And so on and so forth. It's probably too long a message already, but basically "kurios" was not "adonai", and it's
not inherently some divine title. There is no inherent divinity or even royalty in owning a vineyard or inheriting an estate.
In fact, actually I'd say that, on the contrary, not only that doesn't necessarily indicate a connection to Adonai, but actually most of the NT writers don't seem to stick to the same convention at all. They have no problem naming their Lord (Jesus), or using constructs like Lord Jesus which have no parallels to the use of Adonai. They also have no problem saying "God" all over the place.
I'd say that far from being the same use as Adonai, which was used as a substitution, as a way to
avoid using God's name, in the NT it's mostly just a title.
Now don't get me wrong, I would assume they were familiar with the OT, or at least with the Septuagint translation, the way they quote mine it and reproduce even the translation errors from that one, but basically that's where the supportable connection ends. Just because they toss "kurios" left and right, it doesn't mean they're using it exactly as in the Jewish use of "adonai".