Depends how soon you get with the breeder and the relationship etc you have with them. I picked my Buddy's name - had the breeder's affix but the rest was an agreed choice jointly made. But then I'd been working with the breeder so to speak for weeks before the mating let alone the birth.
Some breeders follow naming conventions around the alphabet, films, cars etc etc and so have the KC names for their puppies all sirted and dont like to make any changes but many do.
Often puppies bought from one Affix that then go to another have their name changed to include the new affix. That's where you'll see "so and so so and so
at so and so". The "at" suggests they've been bought into this other affix owners care
For example, if Gilly bought a puppy from Jane it might become Shenmore Beautiful at Glowstar.
If it's something you want to do then ask away.
hth