Pet blessing is done on special occasions, and many pet owners attend the events with their pets.
It's not been done in my locality, though, but I have watched them on tv. Before the priest blessed a pet, he asked for its name. Once the priest approached a little girl, cradling her duck, and asked her for its name, and before she could answer, the duck cried out loud "Quack! Quack!". ("You're a quack minister"! -- interpretation mine.)