Brain-twisting question for the win: are you the same person you were yesterday? Are you sure? Well, you might not be in "The Nose." The great paradox of "The Nose" is that identity is both super-specific and unique and at the very same time totally fluid, depending on what markers the identifier is using. For example, the nose itself is both very easy to recognize (the barber knows whose it is as soon as he sees it), hard to recognize (it manages to escape from its own owner by pretending to be a doctor), and able to create for itself a whole new life apart from its place of origin (to the point that it can even deny being Kovalev's nose right to his face). If identity is really so slippery in this world, then what forms the core of any human being there?
In "The Nose," identity is so fluid that actually the fact that Kovalev emerges as the exact same person at the end of the story is a triumphant happy ending.
Gogol suggests that identity is actually completely static and only seems fluid to those who use primarily external markers as a way of identifying others.