Is someone a vegan when he or she owns a pet for their own fulfilment?
I always say that you can't own an animal. Can you own a human person?
A reasonably broadly acceptable definition of veganism is an effort to avoid exploiting non-human animals for human use.
According to this definition, keeping an animal as a companion "for one's own fulfillment" would perhaps be considered not consistent with veganism.
Many vegans object to the industries that breed animals for human use as pets.
On the other hand, many vegans are animal-lovers and do keep animals. Most of the vegans I know who have "pets" or companion animals living with them do so because the animal was rescued. Often, they have an injury or disability that caused them to be rejected by pet-breeding industries or earlier "owners".
In this situation, keeping the animal might be considered an act of compassion, which is a key principle or driving emotion behind many people's vegan practice.
Of course, if you are keeping an animal, they might require non-vegan food, and then the vegan is put in the awkward position of obtaining such food, which is one of those difficult compromises that inevitably arise for people who commit themselves to an ethics of non-harming. I don't think you'd be able to find a self-professed vegan who's never compromised on something, chosen the lesser of two evils, or acted against strict vegan principles out of basic necessity.