When Jesus was baptized by John the Baptist in chapter three of Matthew, the Trinity (God the Father, God the Son and God the Holy Spirit) was present. In chapter 28 of Matthew, Jesus tells His disciples to baptize His followers in the name of the Father, Son and Holy Spirit.
We are baptized in the name of the Father, Son and Holy Spirit (the Trinity) because they are equal persons of the God we serve. God is Father, Son AND Holy Spirit. One God in three distinct person, yet equal in their deity. They have always been and always will be. They do not need anything or anyone else. They make the same decisions, have the same understanding and act for the same purpose.