If you are playing a vampire, unless you have one of the following traits:
- Inoffensive to Animals merit
- Dots in Animalism
- Dots in Animal Ken
...animals that are not blood bound to you will be terrified of your character. They will not let you pet them, they will not let you come near them. They will run, bite or otherwise attack, because they recognize vampires as the predators they are.
This means is that it is generally not a good idea for you to bring an animal that is bound to you to places that other vampires are. It is, in fact, a very bad idea to do this, because the mortals around will likely be wondering why Fido is howling while desperately trying to get away from the otherwise completely normal looking people around them. This is also hardly a great way to win friends and influence people amongst the vampire community.
Animal Ken can negate this tendency to a point, but Animalism is the better skill to possess in order to be able to interact with animals.
If your vampire has a pet, it's best that other vampires (unless they as well have the above-referenced traits) not ever encounter them.