The common word, as was mentioned in the comments, is the use of the word System. I have seen this in reference to the Jovian, Saturnian, and Plutonian systems, referring to the planet and collection of moons. If one is referring to just the moons, without the planet, usually the word Satellite is injected (Saturnian Satellite System).
It seems this isn't commonly used with Mars, likely as a result of it only having two moons.
Generically, it's called a System. There doesn't seem to be a good word for the system for just the moons. Planetary System refers to the system of planets surrounding a star. I would call it Planetary Satellite System, or something like that, generically.