Montezumas Castle in relation to the actual Montezuma (emperor)? -

I m just wondering why Montezuma s Castle was named so when Montezuma was an Aztec emperor and, from my understanding, never inhabited Arizona.

The well got its name from the mistaken belief that Montezuma, the infamous Aztec chief, actually lived in the nearby ruins known as Montezuma Castle. Since the Aztecs did not settle in this area, there is little doubt that Montezuma ever lived at the castle or set eyes on the well.