Jesus gives us the specific formula to use in the Gospel according to Matthew, as already cited in this thread. In the Acts, it never tells us exactly what was said during the baptism, but simply that baptisms were done, and are to be done, ‘in the name of Jesus’. How can this be reconciled? To do something in the ‘name of somone’ is to do such by that person’s authority. The Church baptizes by the authority of Christ, and baptizes into converts (and infants) into Christ. So in a very real sense, she does ‘baptize in the name of Jesus’. It is by His name that we baptize, but not using the specific name “Jesus” as the baptismal formula.
