A sheriff could say "Open this door!" or "I'm arresting you!", and follow it with "in the name of the Law and of the King!".
He is not implying in any way that the Law and the King are the same thing, much less that they are a single person. He is simply stating the sources of his authority to force the door and make the arrest.
So when Jesus said "baptizing them in the name of the Father, and of the Son, and of the Holy Ghost", he was simply indicating by what authorities they would be performing the baptisms.