Yes, you can ask.
Do be aware, however, of two things:
- Veterinarians are not experts in breed identification. They will write something down, but particularly if your puppy is a rare breed or a mixed breed, don’t take their opinion as gospel.
- Veterinarians do not like being sued for fraud, and it is fraud for them to lie about your dog’s breed on their paperwork. There is a trend for people with a banned breed to get it listed as some other breed on veterinarian paperwork – to get their clearly most pit mix listed as a French Bullpuppy or Terrier or Beagle mix, etc. Please don’t ask your vet to commit fraud.