Different names for a different life, but guess depending on the person probably still uses their original name. If you're John who comes back as Max chances are you'll still respond to John at least early into the new life and before living through too many lives. Now something I want to do but don't have an idea for is a way for a character to identity another after starting a new life, it can't be obvious and see able from a distance, it'll take getting close to the other one, like say a marking.