Same person or different?
Larry Niven's very excellent A World Out of Time took this to another level. The story begins with the protagonist waking up in a strange place and in a "new" body. Then he remembered doing something stupid which had led to his accidental death. Then he remembered having expressed his wish to be cryo-preserved. Then they explained to him that "he" was some criminal whose memory and personality had been wiped and the RNA of some frozen dead person had been introduced to create what they believed to be a new person. The protagonist, Corbell, distinctly remembers his "original" life and struggles to determine whether or not he is now, in fact, the same person with a different body.
That's only a small part of the story, but it's a very interesting premise in a very interesting novel.