Some believe that the only valid way to baptism is “in the name of Jesus.” They deny that it is scriptural to say, “I baptize you in the name of the Father, the Son, and the Holy Spirit.” No one denies that someone must be baptized in the name of Jesus. This simply means that we are baptizing by the authority of Jesus (cp. Colossians 3:17).
There is a corollary in Matthew 28:18-20, Mark 16:15-16 and Luke 24:46-48. The term “name” in Luke 24 is the equivalent to “authority” in Matthew 28, just like the term “preaching” in Luke 24 is the equivalent of “teaching” in Matthew 28. Therefore, Jesus has all authority (i.e. it is done in His “name”) to direct us in every religious act.
Jesus told us to go and baptize people (Matthew 28:19-20). What we do deny is that the Bible tells us what we are to say when we baptize someone. The validity of baptism does not depend on what the administrator says, but on the authority in which it is based.