There was likely much revision in the second century. For instance, in 1 Corinthians 14, it seems the "women be silent" was an interpolation. And Paul never actually wrote 1 Timothy which says the same thing.
Of course, the New Testament is a compilation of books from different Christian groups from the first and second century, each with different theological viewpoints.
But from what Paul and the Christian group he was writing to at Philippi, I think their answer would be found at Philippians 2:9, “Therefore God exalted him to the highest place and gave him the name that is above every name.”
Therefore the name above every name is given to Jesus...the one who in verse 6, who had “God’s form” or nature.
No matter whether the LXX with the divine name was used by the New Testament writers or indeed placed the name in their original writings, often passages in the Old Testament that were about YHWH got applied to Jesus. For these writers Jesus was by nature or kind YHWH, while a distinct person from his Father.
The writer of the epistle of John would have agreed. Of course, the writer of Mark would’ve bitterly disagreed. And likely the writer of Matthew and Luke.
Whatever the original form of the writings that became the New Testament and whether the Divine Name was included, or passages like in Philippians were ramped up and altered to reflect high Christology is still speculation and guesswork.
Until someone finds an early NT manuscript with the divine name in it, there is no real proof.