
I would apply for full registration, as it is a small fee, and will be much more if you want to do it later.
You won't be able to show her until she is fully registered with a name.
If the breeder has not filled out the nameing section, with her affix I would rather doubt you had bought her from a breeder that shows, and is proud of her stock, so wanting her choice of name on the pups. In UK all pups are named by the breeder, and registered at the time the whole litter is registered.
I would normally on a US pedigree (unlike a British one where few Champions are made in a breed each year) expect nearly all her ancestors in her pedigree to be Champions, if they are not in a large part Champion stock, it is unlikley that she has been bred with the breed standeard and shows in mind, and your chances in the show ring will be slim. You can of course compete in all manner of performance events which are fun for you both.