Matthew 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit:
Acts 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins,
We are baptised ‘into Christ’
Romans 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
Galatians 3:27 For as many of you as have been baptized into Christ have put on Christ.
We are born ‘in Adam’.
When we are baptised, we are reborn ‘in Christ’.
1 Corinthians 15:22 For as in Adam all die, even so in Christ shall all be made alive.
Galatians 3:29 And if ye be Christ’s, then are ye Abraham’s seed, and heirs according to the promise.
The form of words to be used at baptism is: -
“You are baptised in the name of Father, and of the Son and of the holy spirit”
Therefore, we are baptised into Christ in the name of the Father, the Son and the holy spirit.
Although we are not told, we might reasonably suppose that at the immersion of those baptised ‘in the name of Jesus Christ’ the form of words used was “You are baptised in the name of father, and of the son and of the holy spirit”.
There is no real contradiction.
There is only one name given under heaven whereby we must be saved.
Acts 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
I hope you find this helpful.