noun

• (uncountable) The quality or state of being anonymous (nameless or unidentified).
  "Now there are twenty-nine skaters on Wollman Rink Circling in singles and in pairs In this vigorous anonymity"
• (countable) That which is anonymous.
  "In one sense the protagonist is the poet himself, but in another sense he is an anonymity."
• (uncountable) The quality or state of being generally unknown, unrecognized, or uncelebrated.
  "The profiteer who through a combine fleeces the public would scorn to wrong a friend or betray those of his own household. The problem then resolves itself into a question of the elimination of the impersonality, the anonymity of modern life that is made an excuse for moral irresponsibility."