Maybe a better question then would be, "How do you identify?" Philosophically the question is far from bullshit. The question is to make you analyze what is yours (what have you actually decided to do) over what society, peers, or family have told you that you should be. We like to play this game on freshmen philosophy students because most of them haven't yet analyzed their entire life to figure out why they are doing what they are doing and who they really are. The point of the exercise is to decide what is your motivation for doing things and acting the way you do.
Take a minute to consider the following questions.
Who are you?
Who are you, really?
Who do you really think you are inside?
It took me a full year to find the answer to these. The answer was that these questions, when posed as philosophical dilemmas, were bullshit. This post is not about ‘understanding who you really are’. It's about understanding, 'who you really are'.
“Who are you” is a question that sounds grandiose. It’s hard to come up with a philosophically solid answer, and this makes it seem interesting. It is not interesting. It just lacks context.
What would you say if you were asked “who are you?” by the police? By a doctor? By a relative? By a potential boss? By a space alien?
You should say different things, because these people would be using the same words to mean different things.
What they really want is information about you that is of decision relevance to them. A police cares where you are from. The doctor cares how old you are. A relative cares about who you are related to. A boss cares what skills you have. A space alien cares about your number of eyes and hands. “Who are you?” really means, “given your understanding of my position, what simple information about yourself do you think is useful to me?”
So when a young philosopher follows up your response with, “no really, who are you?”, you should respond with asking, “what in particular would you like to know?”
Some may respond to this saying that there does exist a true self. A real self. This is what the phrase should really mean, and this is what I personally spent a year pondering.
But first, the very idea of there being a true self is specific to a set of religions and philosophies that you may not believe in. If you’re a empirical atheist, you shouldn’t. David Hume fought the notion of an inner self 250 years ago. [1] Derek Parfit fought it more concretely in the last 30 years. [2]
Second, even if you do ascribe to a belief system where there is some sort of true self, this would not give you a clear way to describe it. Should you say that you are a Capricorn inside? Or that a small fraction of your brain believes in Libertarianism? Or that you possess soul #988334?
Of course not. The question of “who are you?” is wrongly worded, and the one of “who are you, really?” should be placed on hold until the questioner can figure out what they are actually trying to ask.
[1] David Hume's view on Personal Identity, Skinner (2013)
[2] Reasons and Persons, Parfit (1986)