Cislunar spaceEarth's gravity keeps the Moon in orbit at an average distance of 384,403 km (238,857 mi). The region outside Earth's atmosphere and extending out to just beyond the Moon's orbit, including the Lagrangian points, is sometimes referred to as cislunar space.[109]
Based on just the thread title, I'd say "the universe".
I think the space around any planet should be called planetary space and the rest of stellar space around a star should be interplanetary space, Then you would have Earth's planetary space, Mars' planetary space, Jupiter's planetary space, etc. This would fit in convention with the space between stars in a galaxy being called interstellar space. If you call the volume of space containing a galaxy galactic space. Then you continue with convention of our universe being made up of galactic space and intergalactic space. The space around a moon could be called moon space or lunar space (in the case of Earth's Moon) and is part of a planet's planetary space. Maybe each volume boundary should be the volume limits to which a small mass satellite could orbit around the body in question for more than one orbit for any inclination or eccentricity. This would probably allow for a fairly consistent way to identify space volume boundaries for any object or group of objects in the universe.