God is Holy and his Spirit is therefore Holy. In the Scriptures, the term "Holy Spirit" or "Holy Spirit of God" is synonymous with "Spirit of God" or simply "the Spirit" and even "finger of God." We can see this truth by a simple comparison of passages.
"The Spirit of God descending as a dove and coming upon him" (Matthew 3:16).
"The Spirit as a dove descending upon him" (Mk 1:10).
"The Holy Spirit descended upon him in bodily form as a dove" (Luke 3:22).
"I saw the Spirit descend as a dove from heaven, and it remained on him. I myself did not know him; but he who sent me to baptize with water said to me, "He on whom you see the Spirit descend and remain, this is he who baptizes with the Holy Spirit.'" (John 1:32-33).
"But if I cast out demons by the Spirit of God, then the kingdom of God has come upon you" (Mt 12:28).
"But if I cast out demons by the finger of God, then the kingdom of God has come upon you" (Luke 11:20).
"Do not grieve the Holy Spirit of God, by whom you were sealed for the day of redemption" (Eph 4:30).
"But when they hand you over, do not worry about how or what you are to say, for it will be given you in that hour what you are to say. For it is not you who speak, but it is the Spirit of your Father who speaks in you" (Matthew 10:20).
When they bring you before the synagogues and the rulers and the authorities, do not worry about how or what you are to speak in your defense, or what you are to say, for the Holy Spirit will teach you in that very hour what you ought to say." (Luke 12:12).