How do I find out my neighbours name, when they're not on the electoral register?

My neighbours dog attacked mine causing him to require veterinary treatment. She has refused to pay the vet's bill. Now I intend to take her to small claims court but cannot do so without her surname. She's not on the electoral register (I already paid to find out) and now I'm heading down a dead end. Is there anyway I can find it out without, obviously, breaking the law.