This is like that Seinfeld episode where Elaine’s coworker mistakenly refers to her as “Susie,” and Elaine decides it’s easier to live a double life than try to correct her.
Should we just stick with “Machu”? Smallpox and Spaniards pretty much wiped out anyone who might object. On second thought, though, maybe that’s reason enough to change the name.
Side note: Bingham’s Lost City of the Incas, the 1948 book about his discovery of Machu Huayna Picchu, is a great read.