
Hi I think the rules are different in USA and UK.
I know that in USA that the owner can choose the dogs name if the breeder has not stipulated the choice, as In USA the litter is registered, and then the owner applies for individual registration.
Here in UK only the breeder can register the pup, and this is normally done at around two weeks of age all together. the litter registration form has boxes for each pup where two choices of name have to be given.
Also it is at this point that Endorsements (restrictions on registering progeny or exporting) are added, and many responsible breeders use these so that the new owners cannot register puppies from their stock without reference to them first. This is usually to ensure that they do the relevant health tests and will be responsible breeders.
I keep my registered names short just the affix (Barbelka) and one word, usually starting with the same letter of the alphabet for each litter. some breeders use themes for each litter.
They all have short call names of only four letters long at home.