An identity by its very definition is

There are 4 definitions. 2 of which have sub-definitions. You're using the definition most associated with "individuality". If you use the one most associated with identification, you would see it as:

2 a : psychological orientation of the self in regard to something (such as a person or group) with a resulting feeling of close emotional association
b : a largely unconscious process whereby an individual models thoughts, feelings, and actions after those attributed to an object that has been incorporated as a mental image