If the dog requires some specialty medication (fillable at a specialty pharmacy), the veterinarian will make the prescription to whatever name the owner claims.
My guess is that somehow created enough of a paper trail for the election registrar to allow the registration.
At my pharmacy, we include the person’s first name next to the last name. There is also a drop-down menu to list the new entrant as human or animal, so pets aren’t be entered in as people.
I mean, sometimes people mess up, especially when new, and they get put in as a person. That usually gets fixed by the pharmacist five minutes later unless they have a human-sounding name and not one like, “Scruffles.”