Yes. Gift, taken personally in God, is the proper name of the Holy Ghost because the Holy Ghost receives His proper name from the fact that He proceeds from Father and Son.
A gift is properly an unreturnable giving, as Aristotle says (Topic. iv, 4)--i.e. a thing which is not given with the intention of a return--and it thus contains the idea of a gratuitous donation.
Now, the reason of donation being gratuitous is love; since therefore do we give something to anyone gratuitously forasmuch as we wish him well.
So what we first give him is the love whereby we wish him well.
Hence it is manifest that love has the nature of a first gift, through which all free gifts are given. So since the Holy Ghost proceeds as love, He proceeds as the first gift.