There appears to be a correlation. It does have a kink in it though. It appears to be an allusion to this verse:
[Isa 62:1-5 KJV] (1) For Zion's sake will I not hold my peace, and for Jerusalem's sake I will not rest, until the righteousness thereof go forth as brightness, and the salvation thereof as a lamp that burneth. (2) And the Gentiles shall see thy righteousness, and all kings thy glory: and thou shalt be called by a new name, which the mouth of the LORD shall name. (3) Thou shalt also be a crown of glory in the hand of the LORD, and a royal diadem in the hand of thy God. (4) Thou shalt no more be termed Forsaken; neither shall thy land any more be termed Desolate: but thou shalt be called Hephzibah, and thy land Beulah: for the LORD delighteth in thee, and thy land shall be married. (5) For as a young man marrieth a virgin, so shall thy sons marry thee: and as the bridegroom rejoiceth over the bride, so shall thy God rejoice over thee.
In context Isaiah is referring to Jerusalem/Zion.
However, if you isolate verse 2 it seems to work as a separate messianic prediction.
But that solution kind of has a smell to it.
Alternatively it serves of a pattern/shadow of something to be fulfilled by the messiah and is, in Revelation.
Alternatively it suggests that Christ is in some sense the new Jerusalem, just as the new Jerusalem is in some sense the new Covenant:
[Gal 4:24, 26 NASB] (24) This is allegorically speaking, for these women are two covenants: one proceeding from Mount Sinai bearing children who are to be slaves; she is Hagar. ... (26) But the Jerusalem above is free; she is our mother.
Or, the new name could be those predicted for new Jerusalem because Jesus became married to the new Jerusalem; his bride, the 144,000 lost sheep of Israel and Jesus was unmarried until then:
[Isa 62:4 KJV] (4) Thou shalt no more be termed Forsaken; neither shall thy land any more be termed Desolate: but thou shalt be called Hephzibah, and thy land Beulah: for the LORD delighteth in thee, and thy land shall be married.
Beyond that, as Ozzie points out, perhaps it is not revealed.
[Rev 19:12 NASB] (12) His eyes are a flame of fire, and on His head are many diadems; and He has a name written on Him which no one knows except Himself.
Of course, Paul is the steward of God's secrets to dispense them to the gentiles during the climax of the Jewish age. Perhaps he inherited his father's name, as taught by Paul and Hebrews.