The word translated multiple times in Rev 3:12 as "name" (ὄνομα) would in my ever so humble opinion better be translated as "title" or "handle".
YLT Rev 3: 12He who is overcoming—I will make him a pillar in the
sanctuary of my God, and without he may not go any more, and I will
write upon him the name [ὄνομα] of my God, and the name [ὄνομα] of the
city of my God, the new Jerusalem, that doth come down out of the
heaven from my God—also my new name [ὄνομα].
Young, R. (1997). Young’s Literal Translation (Re 3:12). Bellingham,
WA: Logos Bible Software.
This is a reference to the fact that in the OT God was referred to by the Tetragrammaton and "the LORD" while the post-resurrection title for God is "the God and father of our lord Jesus the Christ," or "the Father" for short and Jesus is now called "the lord".
The Father:
BSB
2 Cor 1: 2Grace and peace to you from God our Father and the Lord
Jesus Christ. 3Blessed be the God and Father of our Lord Jesus Christ,
the Father of compassion and the God of all comfort,
Ephesians 1:3 Blessed be the God and Father of our Lord Jesus Christ,
who has blessed us in Christ with every spiritual blessing in the
heavenly realms.
Colossians 1:3 We always thank God, the Father of our Lord Jesus
Christ, when we pray for you,
1 Peter 1:3 Blessed be the God and Father of our Lord Jesus Christ! By
His great mercy, He has given us new birth into a living hope through
the resurrection of Jesus Christ from the dead,
And Jesus, the post-resurrection son of God and lord (his new title):
Heb 1: 4 So he became as much superior to the angels as the name he
has inherited is superior to theirs. 5 For to which of the angels
did God ever say, “You are my Son; today I have become your
Father” ? Or again, “I will be his Father, and he will be my
Son” ?
New International Version Acts 2:36 "Therefore let all Israel be
assured of this: God has made this Jesus, whom you crucified, both
Lord and Messiah."
BSB Philippians 2: 9Therefore God exalted Him to the highest place,
and gave Him the name [title] above all names, 10that at the name
[title] of Jesus every knee should bow, in heaven and on earth and
under the earth, 11and every tongue confess that Jesus Christ is
Lord, to the glory of God the Father.…