Speaking "in the name of" something does not necessarily mean that one is speaking of the name of a personality. A cliché we hear frequently in old crime movies illustrates this. Sometime during the film, a policeman invariably comes running out with his gun drawn and aimed at the suspect, and he says, "Stop in the name of the law!" Does the law have personality? Is it a personality? No, it is an inanimate thing. The policeman was commanding the robber to stop in the name of an authority, the law.
So just because the baptism formula includes within it the authority of the Father, Son, and Holy Spirit does not mean that the Holy Spirit is a Person. It is mentioned, undoubtedly, as the means through which the repentant sinner is brought to the point of being baptized. God tells us clearly that the Holy Spirit is given to convict us of sin (John 16:8-9). God stirs up our minds by the power of His mind, using His Spirit to lead us to think of things in a way that we never have before, and He thereby brings us to repentance.
By the same means, He also reveals to us the real Jesus, and by the same means, He gives us the power to believe in Jesus Christ for the forgiveness of sin. The Holy Spirit, then, is the power that God uses to bring us to that point.
John W. Ritenbaugh
The Holy Spirit