Is there a timekeeping word for the orbit of a moon? For a planet, we can colloquially refer to its period of rotation as a "day" and its period of revolution around its parent star as a "year." Some worlds have unique terms, such as Martian days being referred to as "sols", but the principle is the same: one word for rotation around its axis, another for revolutions around the star.

Is there an equivalent word for the period of a moon's revolution around a planet? On Earth it roughly lines up with a "month," but multi-moon planets would have different periods for each moon. 

If I was in charge of timekeeping for a mission to Europa or Ganymede, what term would I use to refer to the period of time it takes for the moon to complete one orbit of Jupiter?
You should use one of the precisely defined terms of specific measures of orbital period, which are described on this Wikipedia page.

You might get away with just "orbital period" is you're not using it in a context that requires precision.

For length of day there's synodic day as well as sidereal period.  There's a discussion on the difference between these here.