> The hints don't show a source.
Then I would suggest that you disregard them. I do not have the latest edition (2006) of MF4 (Edward Fuller), but earlier editions showed that his wife's name is unknown.
> Does anyone know where the name Ann came from?
It has been kicking around for over a century. In his "Genealogy of Some Descendants of Edward Fuller of the Mayflower" (Palmer, MA: The Compiler, 1908) William Hyslop Fuller wrote "The name of the wife of Edward^1 Fuller, though sometimes given as Ann, is really wholly unknown."
Dale H. Cook, Member, NEHGS and MA Society of Mayflower Descendants;
Plymouth Co. MA Coordinator for the USGenWeb Project
Administrator of
http://plymouthcolony.net