4 He is called the Spirit, according to the Scripture just now read, For to one is given by the Spirit the word of wisdom. He is called the Spirit of Truth, as the Saviour says, When He, the Spirit of Truth, has come. He is called also the Comforter, as He said, For if I go not away, the Comforter will not come unto you. But that He is one and the same, though called by different titles, is shown plainly from the following. For that the Holy Spirit and the Comforter are the same, is declared in those words, But the Comforter, which is the Holy Ghost; and that the Comforter is the same as the Spirit of Truth, is declared, when it is said, And I will give you another Comforter, that He may abide with you for ever, even the Spirit of Truth; and again, But when the Comforter has come whom I will send unto you from the Father, even the Spirit of Truth. And He is called the Spirit of God, according as it is written, And I saw the Spirit of God descending; and again, For as many as are led by the Spirit of God, they are the sons of God. He is called also the Spirit of the Father, as the Saviour says, For it is not you that speak, but the Spirit of your Father which speaks in you; and again Paul says, For this cause I bow my knees unto the Father, and the rest;... that He would grant you to be strengthened by His Spirit. He is also called the Spirit of the Lord, according to that which Peter spoke, Why is it that you have agreed together to tempt the Spirit of the Lord? He is called also the Spirit of God and Christ, as Paul writes, But you are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. But if any man have not the Spirit of Christ, he is none of His. He is called also the Spirit of the Son of God, as it is said, And because you are sons, God has sent forth the Spirit of His Son. He is called also the Spirit of Christ, as it is written, Searching what or what manner of time the Spirit of Christ which was in them did signify; and again, Through your prayer, and the supply of the Spirit of Jesus Christ.
Source: Catechetical Lectures (New Advent)