Objection 1. It would seem that "Love" is not the proper name of the Holy Ghost. For Augustine says (De Trin. xv, 17): "As the Father, Son and Holy Ghost are called Wisdom, and are not three Wisdoms, but one; I know not why the Father, Son and Holy Ghost should not be called Charity, and all together one Charity." But no name which is predicated in the singular of each person and of all together, is a proper name of a person. Therefore this name, "Love," is not the proper name of the Holy Ghost.
Objection 2. Further, the Holy Ghost is a subsisting person, but love is not used to signify a subsisting person, but rather an action passing from the lover to the beloved. Therefore Love is not the proper name of the Holy Ghost.
Objection 3. Further, Love is the bond between lovers, for as Dionysius says (Div. Nom. iv): "Love is a unitive force." But a bond is a medium between what it joins together, not something proceeding from them. Therefore, since the Holy Ghost proceeds from the Father and the Son, as was shown above (Question 36, Article 2), it seems that He is not the Love or bond of the Father and the Son.
Objection 4. Further, Love belongs to every lover. But the Holy Ghost is a lover: therefore He has love. So if the Holy Ghost is Love, He must be love of love, and spirit from spirit; which is not admissible.
On the contrary, Gregory says (Hom. xxx, in Pentecost.): "The Holy Ghost Himself is Love."
I answer that, The name Love in God can be taken essentially and personally. If taken personally it is the proper name of the Holy Ghost; as Word is the proper name of the Son.
To see this we must know that since as shown above (27, 2,3,4,5), there are two processions in God, one by way of the intellect, which is the procession of the Word, and another by way of the will, which is the procession of Love; forasmuch as the former is the more known to us, we have been able to apply more suitable names to express our various considerations as regards that procession, but not as regards the procession of the will. Hence, we are obliged to employ circumlocution as regards the person Who proceeds, and the relations following from this procession which are called "procession" and "spiration," as stated above (27, 4, ad 3), and yet express the origin rather than the relation in the strict sense of the term. Nevertheless we must consider them in respect of each procession simply. For as when a thing is understood by anyone, there results in the one who understands a conception of the object understood, which conception we call word; so when anyone loves an object, a certain impression results, so to speak, of the thing loved in the affection of the lover; by reason of which the object loved is said to be in the lover; as also the thing understood is in the one who understands; so that when anyone understands and loves himself he is in himself, not only by real identity, but also as the object understood is in the one who understands, and the thing loved is in the lover. As regards the intellect, however, words have been found to describe the mutual relation of the one who understands the object understood, as appears in the word "to understand"; and other words are used to express the procession of the intellectual conception--namely, "to speak," and "word." Hence in God, "to understand" is applied only to the essence; because it does not import relation to the Word that proceeds; whereas "Word" is said personally, because it signifies what proceeds; and the term "to speak" is a notional term as importing the relation of the principle of the Word to the Word Himself. On the other hand, on the part of the will, with the exception of the words "dilection" and "love," which express the relation of the lover to the object loved, there are no other terms in use, which express the relation of the impression or affection of the object loved, produced in the lover by fact that he loves--to the principle of that impression, or "vice versa." And therefore, on account of the poverty of our vocabulary, we express these relations by the words "love" and "dilection": just as if we were to call the Word "intelligence conceived," or "wisdom begotten."
It follows that so far as love means only the relation of the lover to the object loved, "love" and "to love" are said of the essence, as "understanding" and "to understand"; but, on the other hand, so far as these words are used to express the relation to its principle, of what proceeds by way of love, and "vice versa," so that by "love" is understood the "love proceeding," and by "to love" is understood "the spiration of the love proceeding," in that sense "love" is the name of the person and "to love" is a notional term, as "to speak" and "to beget."
Reply to Objection 1. Augustine is there speaking of charity as it means the divine essence, as was said above (here and 24, 2, ad 4).
Reply to Objection 2. Although to understand, and to will, and to love signify actions passing on to their objects, nevertheless they are actions that remain in the agents, as stated above (Question 14, Article 4), yet in such a way that in the agent itself they import a certain relation to their object. Hence, love also in ourselves is something that abides in the lover, and the word of the heart is something abiding in the speaker; yet with a relation to the thing expressed by word, or loved. But in God, in whom there is nothing accidental, there is more than this; because both Word and Love are subsistent. Therefore, when we say that the Holy Ghost is the Love of the Father for the Son, or for something else; we do not mean anything that passes into another, but only the relation of love to the beloved; as also in the Word is imported the relation of the Word to the thing expressed by the Word.
Reply to Objection 3. The Holy Ghost is said to be the bond of the Father and Son, inasmuch as He is Love; because, since the Father loves Himself and the Son with one Love, and conversely, there is expressed in the Holy Ghost, as Love, the relation of the Father to the Son, and conversely, as that of the lover to the beloved. But from the fact that the Father and the Son mutually love one another, it necessarily follows that this mutual Love, the Holy Ghost, proceeds from both. As regards origin, therefore, the Holy Ghost is not the medium, but the third person in the Trinity; whereas as regards the aforesaid relation He is the bond between the two persons, as proceeding from both.
Reply to Objection 4. As it does not belong to the Son, though He understands, to produce a word, for it belongs to Him to understand as the word proceeding; so in like manner, although the Holy Ghost loves, taking Love as an essential term, still it does not belong to Him to spirate love, which is to take love as a notional term; because He loves essentially as love proceeding; but not as the one whence love proceeds.
Source: Summa Theologica (New Advent)