In Mexico, we've always called him Moctezuma. It wasn't until I started to play Civilization that I discovered that he's known as Montezuma. This sounds very odd because "Monte" means "hill." I do not think hill has anything to do with th name, but it does make it sound funny.
This is the historical linguistics explanation. There may be a textual series of events that will illustrate the timing of the steps, but that specific part I can't address.
Different languages have different rules about permissible sound combinations. You can violate these rules, but such violations aren't really stable. Foreign names – having come from languages with different sounds and different allowed combinations – often cause such conflicts in English.
"Moctezuma" in Spanish and the original nahuatl
Actually in the case of Mo[c/n]tezuma, neither are what the name was/is in Nahuatl. A better approximation would be Moteoc-zoma.
In Spanish, the c and the t switched places in Spanish. This is called metathesis, and is common cross-linguistically. Think "comfortable" pronounced "comfterble" for some English speakers; the T and R swapped.
In English, the C is gone. Assuming it came into English via Spanish, /okte/ isn't a common string in English. /onte/ is more common, with monte as "hill" being a common example.
As to where N came from, there are a lot of cases of what are called intrusive os epenthetic sounds. Tom's son > Tomson > Tompson is an example with P. N and T are made in the same place in the mouth. M and P are as well. P comes in as your tongue position transitions from M to S in Thompson. N comes in when your tongue moves from the O in Mote to T.
In a lot of English words this wouldn't happen because we also have a "rule" about voicing. When between vowels, T becomes like D, unless there's a good reason it shouldnt. Modi-zuma would be the alternative. T remains unvoiced, and so not a tap, and so not becoming so much like D. Since it's more prolonged (by not being tapped), and since voicing is still there as the O part wraps up, you end up with an intrusive N sound, hence Montezuma.
Metathesis (switching order) is a common adjustment. Epenthesis (adding sounds) is a common adjustment as well. Both are common in loanword adaptation around the world, because each language is potentially working with a different set of tools than a language it might be borrowing from.
Hope that all makes sense. I've tried to keep it straightforward. Let me know if you want anything cleared up.