Hero was a dog that belonged to Podrick Payne when he was little.
A Feast for Crows
While Brienne of Tarth and her companions are travelling with Septon Meribald through the riverlands, Podrick asks what Dog’s name is. Meribald replies that he has not told him his name so he calls him Dog. Pod thinks about that for a while and then mentions that he used to have a dog when he was little and he called him Hero. When Meribald asked Pod if Hero was a hero, Pod replied no, but he was a good dog.