There is a post credit scene in the film in which it is shown that the pic/ name of the existing dead girl and details of murder change to another girl's that was actually the main protagonist of this film, Asuka Morisaki. It was mentioned in the movie that the the girl and the boy, Takahiro Ise, had gone to an amusement park in childhood and though they came back safely in this film, it is implied that the red person changes the events and will be killing the girl in the amusement park. This opens possibility of a sequel.
The name of the film is a double meaning. 1. The film is about forgetting the events of that time-loop day, but the lead two players are able to overcome that and are able to remember the events - hence Remember. 2. Also, cutting something to pieces is to "Dis-member", thus "Re-Member" has to mean putting/ joining the previously cut pieces together, that is the actual plot of the film, though no such word with this connotation actually exists in English language. I find that very creative and clever play with words.