Unlikely imho. We struggle with recovering human remains from places like mt everest, on planet earth https://allthatsinteresting.com/mount-everest-bodies . Of course, we'd be able to do it, but I doubt they'd consider it worth the cost.
@retr0id also, rich people on earth pay to have their ashes scattered in space (https://www.ashesinspace.co.uk/ ). If I was an astronaut, being "buried" in space would be pretty cool and I'd probably write that in my will.
@retr0id from a practical point of view, they won't have a crematorium on the Moon. Maybe they could "rig something up." But for the very first death? It'll be way easier on everyone to just ship the body back.
Obvious yes, IMO.
Short run - government astronauts. If someone dies than whichever government sent them will bring their body home because that's where their 'loved ones' are.
Medium term - commercial moon base. Same story. You're not a permanent resident, of course your body is sent back.
Long term - colony. Someone will die in first generation, they'll get sent back. The moon isn't far, everyone will still have super-strong ties with Earth.
You'd have to have somone who's born and raised on Luna to be like, "This is my home. Bury me here."
@strutheo that would have to be one hell of an accident for their body to not be reachable eventually. Most likely cause of death will be a suit malfunction, or something boring like a heart attack while hanging around the base.