I was raised in a oneness Pentecostal church and was taught that baptism in Jesus name was the only legitimate form of baptism according to Acts 2:38. Some believed it was necessary for salvation while some believed it was necessary to be included in the bride of Christ which is a step above being just children of God. I have come to believe that baptismal regeneration is not salvific. I appreciate you bringing out the Greek language in Acts 2:38. This just adds better argument for baptism as obedience, and not justification.
But I would like to know scriptural arguments on why we baptize in the name of the Father, Son, and Holy Spirit. How do we say use the formula in Matthew 28:18-20 while Acts 2:38 uses just Jesus name?
That is a really good question. If you will check netbible.org, Thomas Constable gives a good explanation, which I quote here:
Was Peter violating the Lord Jesus’ instructions when the apostle told his hearers to be baptized in the name of Jesus Christ alone? Jesus had commanded His disciples to baptize “in the name of the Father and the Son and the Holy Spirit” (Matt. 28:19). I do not think so. When Jesus gave the Great Commission, He had in view the discipling of the nations: everyone. When evangelizing non-Christians, it was necessary to have them identify with the triune God of Christianity through water baptism. Peter’s audience on the day of Pentecost, however, was Jewish. They needed to identify with the true God too, but identification with Jesus Christ is what Peter stressed since baptism in the name of Jesus would have been a particular problem for Jews. It meant acknowledging Jesus as their God. Jews already accepted the fatherhood of God and the idea that God is a Spirit.