I just thought “A Skywalker” could be an interesting answer, because you could interpret it as Rey taking the last name, or that she is creating a new order called “Skywalker” and she is claiming that title. Maybe that would seem contradictory or redundant after Rey saying “I’m a Jedi” at the climax.
That’s something I’ve been very strongly considering for the end of my edit as what Rey & Ben call their school of Force students.
A possibility is Rey would be on Tatooine at the Skywalker homestead and like the scene above (without the ghosts; Rey is probably looking at Leia about to land on Ach-to where Ben had trashed his TIE fighter after mindwiping the First Order command staff and defecting), the old woman comes up and says the place is empty & no one stays because of raiders. Rey says she’s here to help. The old woman asks who she is, and Rey answers that she’s a skywalker.
It’s a cool word, it kinda works as a description of a Jedi-type wandering monk, and it honors the whole Skywalker lineage without having Rey kinda presumptuously adopt herself into it.