I didn't even think of Rachel Grey, which would be a very welcome twist. I've been following the behind the scenes stuff quite a bit on this and that character is more likely than not going to be X-23/Laura Kinney, who is a clone of Wolverine and that was set up in the post credit scene in X-Men Apocalypse. Bryan Singer has said that's who the little girl is but no one actually involved in the writing or directing or acting in Logan has confirmed her to be X-23.
The foX-Men films have such a poorly handled timeline that it's hard to pinpoint who some characters may end up being without the studio confirming it. This film is supposed to be set in 2024, which is 2-3 years after the epilogue future scene in Days of Future Past, but the post credit scene from Apocalypse where Mr Sinister/Nathaniel Essex's company takes Wolverine's blood samples was from 1982. So it's taken about 30 years to successfully clone him, since she's supposed to be between 11-14 in "Logan". It sets her up for future movies but from the looks of this film there won't be any future movies involving the older X-Men. Also Apocalypse gave off the vibe they'd continue with that cast if they do any more films, which would take place in the 80's or early 90's I'd guess if they're keeping the same actors from First Class, DoFP, and Apocalypse. The directer of Logan has confirmed when this movie is set, 2024, which is 2 years after the DoFP epilogue so Professor X somehow ages about 20 years in 2 and Wolverine's healing factor is broken. It wouldn't be that muddled if they didn't include the future scene at the end of Days of Future Past.
