Us all having nicknames of animals sounds like a pretty fun idea. I think I would go for kitten personality, as I look innocent, but I have razor sharp claws. If we can all choose our own animal names then this works! If chosen by others, perhaps not as there is a chance of people being offended by the choice.
No, we should not all name ourselves after animals, like Pitbull, because it would be very confusing. A name like that is entertaining for a pop star, but for the rest of us, like at school or work, a person with a name like that is not taken seriously. We should have names that are professional.
If we were all to name ourselves after animals where would it stop! There are only so many animal names that we could use to describe our personalities, so in order to retain originality we would have to start using unflattering descriptive names such as sloth or warthog! Besides it would make us all look unprofessional - who would employ a surgeon or a lawyer named after an animal!
No, stars like Pitbull are doing a HUGE disservice to animals. Especially stars like Pitbull who, by naming themselves after an animal, propagate negative stereotypes of the animal. Bull breed dogs already have a undeserved bad reputation, when a star clings to that reputation and names himself after an animal that he/she believes to be "dangerous" it keeps the stereotype going.