In Matthew 28:19, Jesus commanded His disciples to baptize in the name of the Father, the Son and the Holy Spirit. Now I know my question will sound silly, but keep in mind that there is indeed a reason behind it. So… what is the name of the Holy Spirit?
This is not a silly question. To ancient peoples, the expression “in the name of” meant by the power and authority vested in. People said, “Halt in the name of the king!” This had absolutely nothing to do with the actual, literal name of the king. Halt in the name of the king meant halt because of the authority of the king and because of the authority delegated to person saying to “Halt!” from the king.
So, when we are baptized in the name of the Father, the Son and the Holy Spirit, it means that we are baptized under the authority of and by the power of God–of God as expressed in the “trinity” of the Father, the Son and the Holy Spirit.
Having answered your main question, it is a bit odd that the Holy Spirit is never given a proper name in the Bible. The Father has a name, sort of. It is YHWH or perhaps Jehovah. This is the name Moses was given when he asked in Exodus 3, God, Lord, Father, El, Adonai, Elohim, are all descriptions, but YHWH is a kind of proper name. Similarly, the Son had a proper name, at least during his incarnated life. It was Jesus. Lord, Christ, Messiah, Son, Savior are descriptions, not proper names, but Jesus was his proper name, at least while he lived on the earth. By the way, Jesus had no “last name” Christ was not his last name, but a description of who he was. It is maybe just a bit surprising that the Holy Spirit has no proper name in the Bible, but he does not. Why not? I suppose that is one of the mysteries of Christianity.
Even if the Holy Spirit had a “name” the command to baptize in the “name” of the Father, Son and Holy Spirit would have nothing to do with the actual “name” of the Holy Spirit.