A part of their identity. A PART of. Someones identity is a million different things. If I consider myself tall, if I consider myself fat, if I consider my hair to be brown, or dark brown, or "dark brown but so dark that it looks black unless I'm out in the sun".
if you ask me about my autism diagnosis and I say "I'm autistic", I'm identifying myself. If I said "I prefer to think of myself as a person with autism", I'd be identifying myself, in a different way. If I refused to refer to myself in relation to my autism at all, because I did not wish to be identified by my disability, then I'd be identifying myself!
When someone goes to an AA meeting and says "I'm John Smith, and I'm an alcoholic", hes identifying himself as an alcoholic! That doesn't mean he wants to be an alcoholic, that doesn't mean he will always be an alcoholic, that doesn't mean his whole personality is related to being an alcoholic and going to Alcoholic Pride Parades. Not every form of identity is the same.
If I write an intro post on a fan forum and say some shit like "Hi, I'm Kiku, I'm 26, I'm a girl and I like Usopp and Zelda games" these are all parts of my identity. That doesn't mean they all have the same weight. Obviously, Zelda games mean more to me than womanhood or being born in 1997 ever will.
Everything about you and everything you've experienced shapes who you are, and your identity is, fundamentally, who you are. Its a billion different things all at once.