Thomas Aquinas

“ I answer that, The word "gift" imports an aptitude for being given. And what is given has an aptitude or relation both to the giver and to that to which it is given. For it would not be given by anyone, unless it was his to give; and it is given to someone to be his. Now a divine person is said to belong to another, either by origin, as the Son belongs to the Father; or as possessed by another. But we are said to possess what we can freely use or enjoy as we please: and in this way a divine person cannot be possessed, except by a rational creature united to God. ”

“ Gift is not so called from being actually given, but from its aptitude to be given. Hence the divine person is called Gift from eternity, although He is given in time. Nor does it follow that it is an essential name because it imports relation to the creature; but that it includes something essential in its meaning; as the essence is included in the idea of person, as stated above (Q [34] , A [3] ) .
Art. 2 - Whether "Gift" is the proper name of the Holy Ghost? Objection 1: It would seem that Gift is not the proper name of the Holy Ghost. For the name Gift comes from being given. ”

“ The name "Gift" imports a personal distinction , in so far as gift imports something belonging to another through its origin. Nevertheless, the Holy Ghost gives Himself, inasmuch as He is His own, and can use or rather enjoy Himself; as also a free man belongs to himself. ”