1 Terry: You being an exact copy of the Steve who died on the rocket raises some serious philosophical questions.
2 Terry: Are you two people, or one person in two bodies? Is consciousness tied to physical form, or transferable?
3 Terry: What do you think, Steve?
4 Steve: Crikey! Some serious what questions?

These sorts of questions are often explored in transhuman and cyberpunk genre fiction, though they can also arise in more traditional science fiction and also fantasy.

And "Steve and Terry" themed fiction, of course.