Jacob is a role, not a name by sprovo

At the end of 6.4 Locke tells Sawyer that he could take the role of being the next Jacob. The way he said it stood out in my mind.

It's also stood out in my mind that the kid in the woods looked like Jacob and Aaron. If we're on a loop then it's perfectly reasonable to think Aaron is Jacob or becomes the next Jacob. I suppose you could say he always becomes Jacob. Why would he change names?

Maybe to hide his original existence from MIB? Maybe the name Jacob basically translates to "Protector or the Island". Maybe we haven't seen Jacob's true form yet.

If we haven't seen his true form yet then we'll soon see Aaron return to the island and he'll most likely become Jacob like Locke has become MIB. The difference is that once time loops Aaron remains as Jacob and Smokey starts over from as someone brought to the island from that current time.

Now why would Littleton be crossed off the list in cave if Aaron is the true Candidate?

Simple, it's to once again throw off MIB. Jacob knows that Aaron is on the island as a child and if MIB realizes that he is the true Candidate then it could all be over. The extent that the Others went to in order to medicate Claire while pregnant also leads to Aaron being very important.

Basically when MIB says Jacob is wasting peoples lives he isn't lying. Everyone else besides Aaron is a hoax in order to get Aaron back in a position to claim himself and restart the loop.