St. Ambrose shows from the Scriptures that the Name of the Three Divine Persons is one, and first the unity of the Name of the Son and of the Holy Spirit, inasmuch as each is called Paraclete and Truth.
132. Who, then, would dare to deny the oneness of Name, when he sees the oneness of the working. But why should I maintain the unity of the Name by arguments, when there is the plain testimony of the Divine Voice that the Name of the Father, the Son, and the Holy Spirit is one? For it is written: “Go, baptize all nations in the Name of the Father, and of the Son, and of the Holy Spirit.” He said, “in the Name,” not “in the Names.” So, then, the Name of the Father is not one, that of the Son another, and that of the Holy Spirit another, for God is one; the Names are not more than one, for there are not two Gods, or three Gods.
132. And that He might reveal that the Godhead is one and the Majesty one, because the Name of the Father, the Son, and the Holy Spirit is one, and the Son did not come in one Name and the Holy Spirit in another, the Lord Himself said: “I have come in My Father's Name, and you did not receive Me, if another shall come in his own name you will receive him.”
133. And Scripture makes clear that that which is the Father's Name, the same is also that of the Son, for the Lord said in Exodus: “I will go before you in My Name, and will call by My Name the Lord before you.” So, then, the Lord said that He would call the Lord by His Name. The Lord, then, is the Name of the Father and of the Son.
134. But since the Name of the Father and of the Son is one, learn that the same is the Name of the Holy Spirit also, since the Holy Spirit came in the Name of the Son, as it is written: “But the Paraclete, even the Holy Spirit, Whom the Father will send in My Name, He shall teach you all things.” But He Who came in the Name of the Son came also certainly in the Name of the Father, for the Name of the Father and of the Son is one. Thus it comes to pass that the Name of the Father and of the Son is also that of the Holy Spirit. For there is no other Name given under heaven wherein we must be saved.
155. At the same time He showed that the oneness of the Divine Name must be taught, not the difference, since Christ came in the oneness of the Name, but Antichrist will come in his own name, as it is written: “I have come in My Father's Name, and you did not receive Me, if another shall come in his own name, you will receive him.”
156. We are, then, clearly taught by these passages that there is no difference of Name in the Father, the Son, and the Holy Spirit; and that that which is the Name of the Father is also the Name of the Son, and likewise that which is the Name of the Son is also that of the Holy Spirit, when the Son also is called Paraclete, as is the Holy Spirit. And therefore does the Lord Jesus say in the Gospel: “I will ask My Father, and He shall give you another Paraclete, to be with you for ever, even the Spirit of Truth.” And He said well “another,” that you might not suppose that the Son is also the Spirit, for oneness is of the Name, not a Sabellian confusion of the Son and of the Spirit.
157. So, then, the Son is one Paraclete, the Holy Spirit another Paraclete; for John called the Son a Paraclete, as you find: “If any man sin, we have a Paraclete [Advocate] with the Father, Jesus Christ.” So in like manner as there is a oneness of name, so, too, is there a oneness of power, for where the Paraclete Spirit is, there is also the Son.
158. For as the Lord says in this place that the Spirit will be forever with the faithful, so, too, does He elsewhere show that He will Himself be forever with the apostles, saying: “Lo, I am with you always, even to the end of the world.” Therefore the Son and the Spirit are one, the Name of the Trinity is one, and the Presence one and indivisible.
159. But as we show that the Son is called the Paraclete, so, too, do we show that the Spirit is called the Truth. Christ is the Truth, the Spirit is the Truth, for you find in John's epistle: “For the Spirit is Truth.” Not only, then, is the Spirit called the Spirit of Truth, but also the Truth, as the Son is also declared to be the Truth, Who says: “I am the Way, the Truth, and the Life.”
Source: On the Holy Spirit (New Advent)