I think it’s likely that it’s named after this deity. They ask the natives what the place is called and they say “amaru-qa” (Land of the flying serpent) https://en.m.wikipedia.org/wiki/Amaru_(mythology)
@577de06dce160a0379163a4bb7b680be3e0a0e1c68de6e6ba8c01134b44064dd I've heard that; it's a stretch. The Spanish didn't enter Inca territory until about twenty years after "America" appeared as a name on the map, with a note about Vespucci. The Incas didn't publish too many books in Europe, and that name isn't even proposed as a source until the 20th century.
In any case, I think the etymology of "Amerigo", the guy's name, is interesting. "Amalrich".