I mean collective identity like "Citizens of X country; mathematicians; skaters; Chinese diaspora; local residents; children". Groups that segments of the population are a part of and about which things like median opinion on a given topic, age, social position, etc. might be said.
Identifying as another individual person is, I think, a symptom of schizophrenia or another psychotic condition if you really mean it. If it's just a thing you say, then that's called lying.