What if a person was baptized "in the name of Jesus Christ"? Should we understand from Acts 2: 38 that the apostles baptized like that, or not?
A valid Baptism is the application of water “in the name of the Father and of the Son and of the Holy Spirit” (Matthew 28:19). Jesus instructed his followers to baptize in the name of the Triune God.
Acts 2:38 does not tell us that the disciples baptized with different wording, substituting “in the name of Jesus” for “in the name of the Father and of the Son and of the Holy Spirit.” Acts 2:38 speaks of being baptized in the manner and by the authority of the one who instituted Baptism: Jesus Christ.
Describing Baptism “in the name of Jesus Christ” stresses the blessings that become one’s own in Baptism: being clothed with the forgiveness of sins Jesus won by his holy life, sacrificial death and triumphant resurrection (Galatians 3:27).