We know that the Lord's words in Matthew 28 were not a formula to be recited, since the disciples always baptized and instructed people to be baptized in the name of the Lord Jesus (Acts 2:38; 8:16; 10:48; 19:5). "In the name of" is not just a recitation, but indicates the authority and power of the risen Christ (Phil 2:10-11). It is in Jesus that we can have the forgiveness of sins during baptism (Col 1:14). Because it is into Christ that we are baptized (Gal 3:27), the baptismal candidate must believe the Lord Jesus is his Lord and Savior and determine to live for Christ all his life. Instead of saying "in Jesus' name," Jesus said "in the name of the Father and of the Son and of the Holy Spirit" to show that all authority that belonged to God had been given to Him.
"Father," "Son," or "the Holy Spirit" are not names. They are titles. The name of the Father and of the Son and of the Holy Spirit is "Jesus" (Jn 5:43; 17:11; 14:26), and there is only one name (singular).
There is no other name under heaven given to men by which we must be saved than the the name of Jesus Christ (Acts 4:10, 12). Only by the name of Jesus is a person cleansed of sin during baptism (Acts 2:38; 10:43).