I hold the Thomistic view: "The principle of individuation, i.e., of numerical distinction of one individual from another with the same specific nature, is matter designated by quantity. Thus in pure spirits there cannot be more than individual in the same specific nature." (Thesis 11, from the 24 Thomistic Theses).
So the soul is individuated through its body. This is the case, even when the soul no longer informs its body body: even then, this soul is still the soul (form) of that body (matter) and of no other.
On Edward Feser's blog Aquinas3000 puts the position this way:
The soul still has a relation to the body as it is the soul of this particular body. It also has its own separate act of esse. The matter individuates it as this particular human being. Once it is separate from the body it is no longer a human being as such, since this refers to the composite. It is an incomplete substance that is capable of subsisting due to its spiritual character that has a relation to this particular body i.e it is the soul of this body.
Some comments later our own Lee Faber replies:
So immaterial human souls have a different principle of individuation out of the body than in the body? So really for Thomas there are lots of principles. At one time it's matter, at another time it's a relation. But a relation requires two fundamenta. How can there be a relation to a non existent (the body)? All you've got is one term and a relation to nowheresville.
First of all I want to clear up the matter of the foundations of relations. Faber's remark, and Scotus' comment reproduced in the first post just cited, "every relative form presupposes something absolute in which it is founded," needs to be qualified. There can be a real relation with one nonexistent foundation, in the case of opinion, memory, anticipation, understanding, will, etc, regarding a non-existent, no-longer-existent, or not-yet-existent object. That is, there can be a real relation between something with subsistent (subjective) being - the mind - and something with merely objective being - the object which exists only in thought and not in itself. However, that's not really relevant to the present case.
In my view, which is the Scotist view, the Thomist account of individuation is involved in insuperable difficulties, which the case of the separated soul merely highlights. Consider the fact that the human body, upon decomposition, no longer exists, while ex hypothesi the human soul continues to exist apart from the body. The matter does not cease to exist, in the sense that prime matter is never naturally created or destroyed according to the principle of the conservation of energy; but individual bodies certainly do cease to exist. This flesh, this blood, these bones, these ashes, this carbon and oxygen, these electrons etc., can all dissembled into their components, be converted to energy and dissipated, and enter into composition with other matter and assume new forms and become new individual substances. This happens all the time. So "this body," the human body that the separated human soul once informed, ceases to exist. As Faber points out, the principle of individuation for an existing concrete substance cannot be something nonexistent, since no non-being can be the real principle of a being. But upon the decomposition of the body, "this" body no longer exists. According to the Thomists, therefore, the separated soul is individuated by something non-existent. But this is impossible, ergo etc.
Perhaps, however, the Thomists do not mean that the soul is individuated by this human body, but by the "signate matter" which individuated the body. So upon the destruction of the body, the "same" matter continues to exist, and the soul is individuated by its relation to this particular bit or chunk or amount of matter which, if it were informing it, would be its body. Sadly, however, this is no better. For the same quantity of matter, when it loses the form of "this" body, takes on some new form. It then becomes a new substance, "this(2)" body, which is numerically distinct from the first "this(1)" body. (Of course what really happens, and which I think strengthens the Scotist case, is that this quantity of matter enters into composition with an indefinite number of new bodies, but talking about it this way is simpler and clearer.) Then, according to the Thomists, this signate matter "this(0)" is the principle of individuation of "this(2)" body; but the principle of individuation for this soul "this(3)" is its relation to "this(1)" body, which is grounded in "this(0)" matter as well. So "this(0)" is the principle of individuation of both "this(2)" and "this(3)", through the latter's relation to the now-nonexistent "this(1)". This sure seems to imply that "this(2)" and "this(3)" are numerically identical, since they share a numerically identical concrete constitutive principle. This is, as a good scholastic would say, inconveniens.
However, a more fundamental objection to the Thomist account arises when we consider the famous Ship of Theseus problem. Any living organic substance, like a constantly repaired ship of Theseus, is constantly excreting old and absorbing new matter. They say - I don't know with how much truth - that we replace all our cells something like every seven years. (In any case particular quantities of matter are exchanged with my environment with every breath, effort, drink, bite, and trip to the restroom.) In that case every seven years all my proximate matter is replaced, and thus of course all my signate prime matter is replaced. But I am the same individual and my body is the same body as it was when I was an infant. Therefore signate matter is not the principle of individuation for my body. Are we really supposed to accept on anyone's authority, even that of a great saint such as St Thomas, that I only remain myself because somehow my body never excretes the little initial collection of atoms making up the chromosomal strings of the sperm and the egg that joined in my conception, and that that self same core of signate matter constitutes my individuality? The notion is absurd. What if that little core were surgically extracted? Clearly I would remain myself. The truth of the matter is that the continuity of the individual existence of any body is insured not by continuous possession of any given bit of matter, or of the whole quantity of its matter, but by the identity and continuity of its form. This is the case even for inanimate bodies, so that souls need not come into it at all. A lake is not individuated by its water; it remains the same lake even though fresh water is continually trickling in and out.
If you want to read more about individuation, the best Scotus texts are in Book VII of the Quaestiones Metaphysicae and in Book II, Dist. III of the Ordinatio, in both of which he discusses a vast range of possible positions and arguments. The best and most comprehensive secondary source is Individuation in Scholasticism, edited by Jorge Gracia. I haven't read all of the latter, I have to admit, despite meaning to get to it for some years now.