There is another theory.
John Cabot, also an explorer, had a Welsh crew who boarded his ship at Bristol, England.
Here is the folk myth: that the name America derives from "ap Meuric," in Welsh meaning the "son of Maurice", says Wikipedia at http://en.wikipedia.org/wiki/Welsh_American/
That leads to this extension: that America was named for Richard Amerike, or Ameryk (see the ap Meuric stem), who was a financial backer of John Cabot's second voyage to the New World, in 1497. Without financial backers, where would America be? Richard ap Meuric, Richard Amerike, Richard Ameryk, see the Wikipedia site.