A famous bearer of the surname was James Madison (1751-1836), one of the authors of the American constitution who later served as president (and after whom Madison Avenue was named).
This name (in various spellings) has been common among European royalty, being borne by ruling queens of Naples, Navarre and Castile. Another famous bearer was Joan of Arc, a patron saint of France (where she is known as Jeanne d'Arc). She was a 15th-century peasant girl who, after claiming she heard messages from God, was given leadership of the French army. She defeated the English in the battle of Orléans but was eventually captured and burned at the stake.
Other notable bearers include the actress Joan Crawford (1904-1977) and the comedian Joan Rivers (1933-2014), both Americans.