I like it as a name, and it means we don't know who the Last Jedi is. It could continue to be Luke (with Rey being something other than a Jedi), it could be Rey (with Luke either dying or turning to the Dark Side) or it could be something else entirely.
Yes. Technically Luke would be the last Jedi, at the moment anyway. Leia never received the training (as far as I'm aware. I guess she might have between films) and Rey isn't a Jedi yet. (We know just having force ability doesn't make one a jedi.) And Kylo is a knight of Ren* not a Jedi. Presumably all the other padawans at Skywalker college are dead.
Of course, once Rey is trained up that would make her the last Jedi, or the first of a new lot. (Or even something else as you say.) 'Last' is often interpreted as final, but it can have an elastic quality. I've got no children, or siblings, so I'm the last of my line (not including cousins - a few of those have kids). But it's possible I might father a child in future, although I doubt it. Either way I'm the last Mardroid right now.
The film title is simple but I think I like it. It does seem to suggest that Luke will be a large focus of the film, which is welcome. I hope they don't kill him off at the end to pass on the baton/lightsaber as it were, since they did that already with Kenobi, and it's become a bit of a cliche in films where mentor types are concerned. It's fine that the new trilogy films follow Rey as the new eyes into this world. She represents the future, but the old needn't be done away with yet.
*And possibly a Sith. Kylo Ren is basically the same thing anyway. Of course we know from the cartoons that there can be other dark-side force-users as demonstrated by The Inquisitors and the bald minx with the two lightsabers, whose name has skipped my memory, with the two Sith lords (Sidious and Dooku**) pulling the strings. I wonder if it turns out that Kylo Ren is just a pawn of that nature and there are actually two sith rather than just Snoke in the background. Probably , not. I think that would be too complicated.
** And of course there was Maul and Savage too, but each group did't consider the other sith.