There is a mounting body of evidence that the continent (originally the area of Newfoundland) is actually named after Richard Amerike, of Bristol.
Amerike was very involved in arranging and aiding the voyages of John Cabot (Giovanni Cabotto) to the new world. In fact, he bore a great deal of the cost of these expeditions, hoping to gain new trade business from the new world.
Cabot's maps were sent to Columbus, and were therefore available also to Vespucci, which is where Waldseemüller got the name from.
Generally, like the city of Washington in the district of Columbia, places are usually given the surname of the person they are being named after, rather than the first name. The obvious exception being royalty, of course, hence Jamestown or Port Elizabeth.
The modern reappearance of this theory is from "Richard Ameryk and the Name America", Hudd, Alfred E., Proceedings of the Clifton Antiquarian Club, 1910.
A more modern, popular reading version is availble in the book "Terra Incognita: The True Story of How America Got Its Name", Broome, Rodney, 2001.