Hmmmm.... Isn't Luke already the last Jedi? And wouldn't that imply Luke would have to die if Rey is to become a Jedi?
Good questions. I feel there's more to the name than the obvious.
Rey could turn bad and join Kylo (unlikely but not impossible)
Luke could bite it and Rey is the last Jedi.
Technically Rey's no Jedi yet. She's not trained in the Jedi ways. Therefore Luke is the last Jedi until Rey is fully trained.