identity

the distinct personality of an individual regarded as a persisting entity; "you can lose your identity when you join the army"

the individual characteristics by which a thing or person is recognized or known; "geneticists only recently discovered the identity of the gene that causes it"; "it was too dark to determine his identity"; "she guessed the identity of his lover"

an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"

exact sameness; "they shared an identity of interests"