I've always been told that the pursuit of personal "identity" with its "personality integration" and "self-realization" was a distinctly modern and Western notion. Perhaps a too-precious conceit of artistes and suchlike.
In recent years, we have even used something called "identity diffusion" as a diagnostic marker. It's a thorny topic that very few people ever think about.
When I meet a new patient (or sometimes just a new person), I never ask "Who are you?" I just ask "Tell me about yourself" or "Tell me about your life." I once met a fellow who told me that he was an "unresolved self." He was one of the most pleasant, well-put-together people I have ever met.
It is often said that psychotherapy and psychoanalysis are about inventing comprehensible, presumably explanatory narratives. Well, our narratives change with time. We evolve with time and experience; sometimes with awareness of our flaws and sometimes with awareness of God.
Some of these topics discussed here: I am not a story: Some find it comforting to think of life as a story. Others find that absurd. So are you a Narrative or a non-Narrative?