Thats a neat twist to the reflecting mirror ideas that a lot of us have. I like it a lot! I think you can make the environments progressively crazier (like using mirrors to ricochet bullets off other objects in the world, etc).
Tbh, I wouldnt worry about the name yet - get the basic mechanics working first and a name will come! (At least thats what Im hoping because I have no name or story for my game lol)