You can register the name with the post office, I believe, but actually I'd recommend against dropping the number for the name entirely! We have just a name, and it's a real hassle with everything from taxis to deliveries - we quite regularly have to stand on the road waving to a lost delivery man. It would be a real problem in an emergency.
Why not put up the name up on the gate, and start informally calling your house 'No 9, Elm Cottage"? I think it's a lovely idea. You might even be able to find some old photos of it in your local library.