Paul said absolutely nothing in Acts 2:38:
“Then Peter said to them, “Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.” (Ac 2:38 NKJV)
As to why Peter said, "be baptized in the name of Jesus Christ," I agree with what John Gill wrote in his commentary on that verse: "in the name of Jesus Christ; not to the exclusion of the Father, and of the Spirit, in whose name also this ordinance is to be administered, Mt 28:19 but the name of Jesus Christ is particularly mentioned, because of these Jews, who had before rejected and denied him as the Messiah; but now, upon their repentance and faith, they are to be baptized in his name, by his authority, according to his command; professing their faith in him, devoting themselves to him, and calling on his name."