When he wrote in Latin, it was "Americus Vespucius". Martin Waldseemüller decided to name the continents after him on his 1507 map, using the feminized Latin version: "the Land of Americus, or America: since both Europa and Asia got their names from women" (thus, America holds the name it was given.) Amerigo was apparently never made aware that a continent had been named for him.
See http://en.wikipedia.org/wiki/Amerigo_Vespucci , http://en.wikipedia.org/wiki/Martin_Waldseem%C3%BCller , and http://en.wikipedia.org/wiki/Naming_of_America#Etymology_and...