There is an identity for the rational soul.
Man is composite with both matter and form. The difference in matter differentiates them in number. The individual soul is proportioned to the individual body. In contrast, and agreement, angels have do not have matter, only form, so each angel is unique (different species).
Summa Theologica 1, Q85, A7: “The difference of form which is due only to the different disposition of matter, causes not a specific but only a numerical difference: for different individuals have different forms, diversified according to the difference of matter.”
(Aquinas) The soul has intellect and will. The habit of knowledge, in the soul, remains after death of the body. The knowledge which resides in the sensitive powers does not remain in the soul.
Summa Theologica 1, Q79, A6: “Thus, therefore, if we take memory only for the power of retaining species, we must say that it is in the intellectual part. But if in the notion of memory we include its object as something past, then the memory is not in the intellectual, but only in the sensitive part, which apprehends individual things.”
In Summa Theologica, St. Thomas Aquinas comments on this in Part I, Q77, A6 and A8:
A6
…the composite is actual by the soul. Whence it is clear that all the powers of the soul, whether their subject be the soul alone, or the composite, flow from the essence of the soul, as from their principle; because it has already been said that the accident is caused by the subject according as it is actual, and is received into it according as it is in potentiality.
A8
I answer that, As we have said already (5,6,7), all the powers of the soul belong to the soul alone as their principle. But some powers belong to the soul alone as their subject; as the intelligence and the will. These powers must remain in the soul, after the destruction of the body. But other powers are subjected in the composite; as all the powers of the sensitive and nutritive parts. Now accidents cannot remain after the destruction of the subject. Wherefore, the composite being destroyed, such powers do not remain actually; but they remain virtually in the soul, as in their principle or root.
So it is false that, as some say, these powers remain in the soul even after the corruption of the body. It is much more false that, as they say also, the acts of these powers remain in the separate soul; because these powers have no act apart from the corporeal organ.
newadvent.org/summa/1077.htm