On the way from Flagstaff to the Phoenix airport we stopped at Montezuma Castle NM, which was set up to protect a 5-story cliff dwelling that between XII and XIVth century was inhabited by Sinagua people.
The naming of Montezuma Well comes from the 1860s explores, who must have thought that these were Aztec ruins and hence called them after great Aztec emperor, Montezuma.
Montezuma Castle:
Castle A (on the left) and Montezuma Castle (on the right):