Baptism in the name of Jesus
I was talking to someone who said they go to the Jesus Church. He said that people in other churches are not baptized because the Bible says we need to be baptized in the name of Jesus Christ, and he gave me these verses from the Bible: Acts 2:38, Acts 8:16, Acts 10:48, Acts 19:5, Romans 6:3, and Galatians 3:27. I know that Jesus said to baptize in the name of the Father, Son , and Holy Spirit. How can I explain these verses to him?
As you noted, Jesus instructed his followers to baptize “in the name of the Father and of the Son and of the Holy Spirit” (Matthew 28:19). Those are the words you will hear at Baptisms today.
The passages cited in your question do 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.” The verses cited in your question speak 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).
On a side note, the Didache, an early second century A.D. writing, speaks of Baptism in the name of the Triune God. The writing provides historical evidence that the practice of the early church was in keeping with Jesus’ instruction in Matthew 28:19.