But, Peter did not baptize literally in the name of the Father, Son, and Holy Spirit.
He did. Unless you want to count all of the Apostles as disobedient to Christ:
Matthew 28:18-20
King James Version (KJV)
18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen.
We know that they were not obedient, so the obvious conclusion would be that there is an equation to what Christ is saying here and what the disciples did.
This takes precedence over what the Apostles actually did. This is ground zero for our instruction, and what we are to be in obedience to.
He baptized in God's personal name, Jesus Christ.
The Name Jesus Christ was not known to men prior to the Son of God being born of Mary.
Jesus is the Name of the Messiah sent unto men.
We do not follow Peter in this. We like the Pharisees replace God's word with our traditions.
There is nothing wrong with obeying Christ's command, lol:
Matthew 28:18-20
King James Version (KJV)
18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth.
19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
20 Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you always, even unto the end of the world. Amen.
That is not a tradition concocted by men, but the very command of Christ. And in that command we must understand the purpose, which is that the disciples would go forth, teaching all Nations about Christ, bringing them into association with Christ and then...teaching them the commandments of Christ.
In that order.
There are much more serious errors in Modern Christendom to deal with that are far more important than how one baptizes men, whether the debate is over which Name to use, or the method of baptism itself. Water Baptism does not save, it is only a symbolic representation of the Death, Burial, and Resurrection of Christ which is then identified to the one professing faith in Christ, and of course their profession of already having been saved.
God bless.