Permanent electronic identification is easy. A grain of rice sized transponder (microchip) is inserted under the skin over the shoulders and remains in position for life. If your rabbit is lost and ends up at a veterinary practice, a rescue centre or at a police station then the microchip will be used to find out the name and phone number of the owner.
No bionic rabbits then, except in science fiction. Actually, in those days, very few owners would want to spend anything on a rabbit. "We can get another for £1.50!" was a common comment. Even if we had Identichips I doubt if anyone would have wanted it for a rabbit. Lots more people care a lot more these days.