So it's not going to be all your ashes and you have to trust that they do actually send them up. My family can do what they like with my remains.
If we ever do colonise the Moon I hope it's not covered in junk by then. The Apollo guys left some crap behind, including actual crap.
I think you get yr own container but yeah I guess on burn up it all gets mingled - but so do all human remains eventually@ and the moon-ll probably be full of all sorts of interesting tat by then!