noun (n)

• the distinct personality of an individual regarded as a persisting entity(noun.attribute)

  Example:
  You can lose your identity when you join the army.
  

  Synonym:
  individuality, personal identity
  

  source: wordnet30
• the individual characteristics by which a thing or person is recognized or known(noun.cognition)

  Example:
  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.
  

  source: wordnet30
• an operator that leaves unchanged the element on which it operates(noun.linkdef)

  Example:
  The identity under numerical multiplication is 1.
  

  Synonym:
  identity element, identity operator
  

  source: wordnet30
• exact sameness(noun.attribute)

  Example:
  They shared an identity of interests.
  

  Synonym:
  identicalness, indistinguishability
  

  source: wordnet30
• The state or quality of being identical, or the same; sameness.(noun)

  source: webster1913