What are the components of your identity? Is there a stable consistent part of you that sustains you regardless of the vicissitudes of fortune?
I'll ask a corollary question (I know, I know, not polite to answer with a question): Does each of us have a unique or multiple identities? I certainly feel like I have a singular identity: Me. But if the world were defining me, I think different people would define me in different ways, depending on how I interact with the particular subject. For example, at work I'm a scientist, and (I hope) a relatively serious one. People there know me as a problem solver, a writer, a teacher and a student, I suppose. In my personal life, my favorite pastime is ice hockey. The good friends I've made from hockey know me as a drunk with a tasteless sense of humor and lack of regard for personal safety.
And of course, just as with all of you, there are other groups whom I interact with in other ways. I don't think anyone can know you beyond how you interact with them, so it might be correct to say that each of us wears many hats and many costumes, depending on the company we keep. I know who I am at hockey, because I put on the number 11 sweater; and I know who I am here, because it says b_b in the top left corner. Each of these things comes with a unique history, context and set of expectations, and I'm therefore not sure that a better-than-superficial answer can ever be given to this question, even though each of us feels like us.
Maybe this is why most people are most comfortable around close friends and family; you don't really need to behave in any particular predefined way.