God is called "Holy" (2 Kings 19:22; Psalm 71:22, 78:41, 89:18; Proverbs 9:10, 30:3; Isaiah 1:4, 5:19, 5:24, 10:20, 12:6, 17:7, 29:19, 29:23, 30:11-15, 31:1, 37:23, 40:25, 41:14-20, 43:3, 43:14-15, 45:11, 47:4, 48:17, 49:7, 54:5, 55:5, 60:9, 60:14; Jeremiah 50:29, 51:5; Ezekiel 39:7; Hosea 11:9-12; Habakkuk 1:12), therefore His Spirit is also naturally called "the Holy Spirit" (Psalm 51:11; Isaiah 63:10-13; Matthew 1:18, 3:11, 12:32; Luke 11:13, Ephesians 1:13, Ephesians 4:30, 2 Peter 1:21).

Some argue when the Son of God is also called "Holy One", it means that he is also God or a member of the "Godhead" (Luke 1:35; Acts 2:27, 13:35 quoting Psalm 16:10; Hebrews 7:26).

This argument ignore the fact that human priests were also called "holy ones" in the Hebrew Old Testament:

Do this: take censers, Korah and all his company; put fire in them and put incense on them before the LORD tomorrow, and the man whom the LORD chooses shall be the holy one. -- Numbers 16:6-7 (ESV)

and

When men in the camp were jealous of Moses and Aaron the holy one of the LORD, the earth opened and swallowed up Dathan, and covered the company of Abiram. -- Psalms 106:16-17 (ESV)

Likewise, believers were also called "holy" in the Greek New Testament:

Therefore, if anyone cleanses himself from what is dishonorable, he will be a vessel for honorable use, set apart as holy, useful to the master of the house, ready for every good work. -- 2 Timothy 2:21 (ESV)

and

As obedient children, do not be conformed to the passions of your former ignorance, but as he who called you is holy, you also be holy in all your conduct, since it is written, “You shall be holy, for I am holy.” -- 1 Peter 1:14-16 (ESV)