A mononym is a term or name consisting of one word only. For example, Madonna or Pele. (The word comes from the Greek roots mono- (one) + -onym (word, name).) Some mononyms are shortenings of full names ("Prince" rather than "Prince Rogers Nelson", for example) while others are adopted as full names in themselves -- I once worked briefly with a woman whose entire name had been legally changed to "Berkana." She told the story of encountering an official who insisted she must have two names, presumably an individual name and a surname, to put on a form, and finally responding "Okay, put "Reverend" and "Berkana." However, an online discussion implies that, at least in the U.S. and U.K., there is no legal requirement that a person have more than a single name. Most, if not all, cultures started out in the past giving only mononyms to people, with surnames or patronymics added later to decrease confusion between people with the same individual name.
Sources:
http://wordsmith.org/awad/archives/0503
http://users.tinyonline.co.uk/gswithenbank/onyms.htm
http://pub122.ezboard.com/fwordoriginsorgfrm11.showMessage?topicID=220.topic