identity

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”

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”