Hi Brittany, it really doesn't matter because AKC papers may worth something to a breeder, for the rest of us folks, it is nothing but a piece of paper. However, there' something else you and your significant other may want to consider. Since the beginning of MyCorgi.com (07), we've had couples who got married and annulled within the same month, bf/gf broke up before the corgi turns one. Re-home due to newborn baby allergic to corgis. I personally had to rehome 2 corgis due to a divorce, foreclosure. There's bf who still share corgi "custody" with his ex-gf...etc.
I know no one wants to discuss about these things, but they are very real. Food for thought, that "last name" may hold significant determine factor in the future. Just like wills, cars, house and finance, you two need to have a serous talk. Good luck!
Frosty was already named before we got him, but personally, I wouldn't use a last name. Most have names that if they included anything it is the breeders name. I would recommend leave off the last name and just register him as "Ruger Red." Then it is not an issue.