What title to put in CV if you do research but unfunded?
If you are a student at a university it's probably unwise to claim to have a title there if you don't have it. Simply putting 'student' is probably better. On the other hand, many departments have unpaid, "zero hour" appointments if you really want an official title.

If you're not at a university and you fund yourself I suppose you can technically give yourself whatever title you want, but "independent researcher" would seem like a fitting description.