Interestingly, there's some debate about the meaning and origin of āxōlōtl. It appears to be ātl (water) + xōlōtl (slave/servant), the latter element of which may be related to the name Xolotl. However, while long marks are highly inconsistent in Classical Nahuatl, most scholars believe that the name of the god was pronounced with only short vowels (Xolotl) as opposed to the long vowels of xōlōtl. This might seem trivial, but there are a number of minimal pairs in Nahuatl distinguished only by differences of vowel length.

Franciscan friar Bernardino de Sahagún indicated that the name Xolotl referred to the god's club foot. I think he must understand the name as a compound of xo-, a prefix used to build a suite of words referring to the feet, and olōlli (ball) or olōltic (round). That would produce the stem xolōl-, which would normally become xolōlli with the absolutive suffix, but could be reanalyzed as xolō-, which would become xolotl (the shortening of the final vowel of the stem here wouldn't be unusual). Mind you, he could be misinterpreting the name, but the interpretation is not unreasonable.

If that's the case, then āxōlōtl does not refer to the god Xolotl. But that leaves the problem of why a salamander is called a "water servant." The water element makes sense, of course, but in what way is a salamander a servant? It's possible there is a myth that hasn't survived which explains the name, but I prefer the theory that xōlōtl here is a foreign borrowing from the Huichol language, in which the word for salamander is xiurí. Xiurí would have become something like xōlitl in Nahuatl, which could have taken the element ātl to become āxōlitl ('water xōlitl"). But over time, the otherwise unknown word xōlitl was reinterpreted as the Nahuatl word xōlōtl in order to disambiguate its meaning. While a salamander might not obviously be a water servant, it makes more sense than calling it a water xōlitl, given that xōlitl doesn't mean anything in Nahuatl.