I've lost myself and the notion of who I am (ego death) several times on trips. And it really makes me think about who I am, and what's really me versus the arbitrary frippery that we use to describe ourselves.
I think the way I try to identify myself is with every single category I am name, age, occupation, gender, hobbies, favorite sports team, spiritual beliefs etc. And that's what I use more or less when I am introducing myself to a person, to keep up with my persona. But as I peel back the layers of who I am, what's a meaningful definition of who I am, gets away from the arbitrary.
Gender tends to stick around, as my anatomy seems to a have say (as well as my sexual interests). My occupation is about the first to go, as I feel that my path in life is somewhat different than what I am currently doing for a living. Though really, I identify myself dependent on the present circumstance. If I'm at work, I certainly identity myself with my profession. If I'm at the beach, with a beer in hand and it's the weekend of a football game, I identify myself differently.
In the end I identify with my purpose in life, and that is to simply be a man who makes the world a slightly better place before he dies.