Does this procedure describe a completely randomized design for this experiment?

Yes, the treatments were randomly assigned to the dogs.
Yes, the treatment groups have the same number of dogs.
No, the veterinarian did not use dogs of the same breed.
No, the names were taken in order, so there was no randomization.

Yes, the procedure does describe a completely randomized design for this experiment. The treatments were randomly assigned to the dogs and the treatment groups have the same number of dogs. Although the veterinarian did not use dogs of the same breed and the names were not randomized, these factors do not affect the randomization of the treatment assignment.