This lack of a definite personhood may be related to the answer that Quirrell gave when Harry asked him why he wasn't like the other children.

[Emphasis added]

I will say this much, Mr. Potter: You are already an Occlumens, and I think you will become a perfect Occlumens before long. Identity does not mean, to such as us, what it means to other people. Anyone we can imagine, we can be; and the true difference about you, Mr. Potter, is that you have an unusually good imagination. A playwright must contain his characters, he must be larger than them in order to enact them within his mind. To an actor or spy or politician, the limit of his own diameter is the limit of who he can pretend to be, the limit of which face he may wear as a mask. But for such as you and I, anyone we can imagine, we can be, in reality and not pretense. While you imagined yourself a child, Mr. Potter, you were a child. Yet there are other existences you could support, larger existences, if you wished. Why are you so free, and so great in your circumference, when other children your age are small and constrained? Why can you imagine and become selves more adult than a mere child of a playwright should be able to compose? That I do not know, and I must not say what I guess. But what you have, Mr. Potter, is freedom.