I agree with everything said above - being a breeder, you have to set some rules to credit your hard work.
The first thing you referred to, pedigree names, is a big one! While I personally focus more on blue-eyed non-showable dwarf bunnies, I do definitely breed a few litters for show as well. especially blue eyed white, as there's not many great typed ones out there. Even though many of my bunnies carry the Vienna gene, they are show quality (structure wise) as I'm still trying to better the breed. Put simply, having your rabbitry name on pedigrees gives you credit for the hard work you put into producing high quality rabbits. It is extremely offensive and disrespectful to change it... Don't get me wrong, you can definitely change the actual name of the bunny, it's just the part that comes before the rabbit's name (title of rabbitry that produced the bunny) that matters. Some breeders, like myself will even offer to include your new name for the bun in the pedigree so it is less confusing! This is seriously a part of my sales policy because some people find nothing wrong with altering pedigrees.
The second point you touched on, pet rabbits being pets only, is also a big topic! There are two different reasons breeders do this, one being to keep the breed standard up, and the other because (unless you have a specific goal) there are plenty of rabbits out there already and breeding should not be something you do spontaneously / randomly for fun. This is why if somebody wants to buy a breeder bunny or a pet that they will occasionally breed, the price does go up at least for my herd because I know you will be profiting from that specific bun. pets are usually priced cheaper, for many obvious reasons - one being that they may not always have the best quality but can still be loved on just as much.
Hopefully this clears any confusion up!