It doesn't have to be to the point where hes going around in disguise like Bridal Mask, Healer or City Hunter, it can also be something similar to Innocent Man, Monster, Shark or Bad Guy. Lastly stories where people take over another persons identity like Rooftop Prince or Please Come Back, Mister. I made a similar post in the past but tweaked it to make it more understandable and with different criteria.

Cain and Abel
The Full Sun
Goodbye Mr. Black
Cinderella Man
Heaven's Order
History of the Salaryman
Personal Taste
Mask, but it's a she
The Legend of Fragrance. all their id's are changed by their parents / foster parents, one doc but also doing investigations with police force he keeps it hidden
East of Eden .... Babies switched at birth by a vindictive nurse, so each is being raised by his family's enemy .... They don't know real identities until much later ... Does it qualify if not done on purpose? .... Also, several side characters hide their identity on purpose (to hide their past)!