As a breeder, I try to make the best decisions possible for my breed. That is particularly important for my breed because it is so rare. The reasons I require my puppies to be registered with my kennel name are:
1. I microchip and register all my puppies with the AKC before they go to their new homes. In my breed, it is important that all puppies in a litter be registered so we can keep track of the number of pups registered per year and breeding trends. The puppies are microchipped and registered with my kennel name plus the buyer's name of choice. This way we have the puppy permanently identified in case of loss, accident, death, and for participation in health testing.
2. It is much easier for other breeders and observers to keep track of breedings, breeding performance, health issues cropping up from certain bloodlines, performance value from certain bloodlines, temperaments of certain bloodlines, and breeding activity of particular breeders if the breeders require using their kennel prefix to register every puppy they breed;
3. Puppy mills and extremely high volume breeders normally do not use kennel names/prefixes because they actually don't want people to find out how many dogs they breed and they do not stand behind their dogs. They want your money and never to hear from you again;
4. I try to breed the best I can and stand behind my dogs. I am proud of what I breed and require my kennel name on my pups' registrations as a further example of my commitment to that particular breeding and to putting my reputation and dedication to the breed on the line. If a person doesn't want a pup with my kennel prefix in its registered name, they apparently don't really believe in me as a breeder. If you don't believe in me as a breeder, don't buy a pup from me. Pretty simple.
5. Oh, BTW, if you have a dog registered with the kennel prefix of a very well-respected breeder, the dog is probably more highly valued by others (both by reputation and monetarily.) In certain breeds, just the kennel name alone will raise the stud fee or puppy price. Certain kennel names equal high value due to a long history of great temperaments, great puppy raising, trainability, performance, longevity, health, etc.