When I was still breeding, I micro-chipped all my puppies before they left for their new homes and instructed the owners to re-register the chips to their names/address. This way even if the new owners fail to register, the chip can be traced back to my vet (and me).
Jingle .. I hope you reconsider chipping your small dog. As Sandy pointed out - dog napping is on the rise, especially small purebred dogs.