Q. 29 “The Divine Persons”
Why “persons”? The answer is that it seems to do best what the previous two analogies of procession and relation do yet more adequately. Aquinas writes:
Thus it is true to say that the name person signifies relation directly, and the essence indirectly; not, however, the relation as such, but as expressed by way of hypostasis. So likewise it signifies directly the essence, and indirectly the relation, since the essence is the same as the hypostasis; but in God the hypostasis is expressed as distinct by the relation, and thus relation, as such, enters into the notion of the person indirectly. (ST 1.29.4)
In short, the word person best expresses at once the unity of the three persons in substance and their distinctness as individuals.
“The individual is what is in itself is undivided, but is distinct from others. Therefore person in any nature signifies what is distinct in that nature… a divine person signifies as relation as subsisting.”
“And this is to signify relation by way of substance, and such a relation is a hypostasis subsisting in the divine nature, although that which subsists in the divine nature is the divine nature itself.” This is a bit like an egg the nest in which the egg is resting is the egg itself.