Martin Waldseemüller was the man who named AMERICA.
He named it after the Florence Italy native, Amerigo Vespucci who had written about his travels to the new world. Martin printed a wood block map with his own invention of a name "AMERICA" across what is now called South America. (See Amerigo Vespucci, about.com).
However it is common, historically-established since people had names, and all-in-all quite proper to call the biggest and most influential member of a set of things by the name of that set. In this case, "America" is a perfectfectly fine alternate way of naming the "United States of America".