Locally-raised troops on Earth were variously called Sepoys, Sowars and Askaris, these terms (and probably others) deriving from corruptions/transliterations of the local usage for a warrior or soldier of some description. I see no reason for the derivation on Mars being any different. But what would the term(s) be? I have never seen anything in the canon that comes close, and the only guide I have is that something with one or more double-vowels would be a good start. So here goes ...
In Parhooni the term for a warrior or soldier is "Sa'anshi" (pl. Sa'anshaya). In the time-honoured tradition of English-speakers everywhere this has become garbled as Sanchi.
Mounted troops are known as "Qua'anshi" (pl. Qua'anshaya), but this term is only ever applied to Canal Martians and never to Hill Martian mercenaries. The Red Men have garbled this as Kwanchi.
The terms for artillery troops are many and various, depending on the type of gun they serve, and even where the gun is located, but the Red Men have cut through this again, calling all such troops Panchis (sing. Panchi), derived from the Parhooni "Pua'anshaya", or gun soldiers.