Orthus

Orthus is a monstrous, two-headed dog residing at the Triple G Ranch. His two heads resemble those of a pitbull's. He is the brother of Cerberus and the Chimera, and his mother is Echidna, while his father is Typhon. In Greek mythology, Orthus was defeated by the hero Hercules on his labor to kill Geryon, the dog's master.

The Battle of the Labyrinth
Orthus had reformed along with Geryon. Although his official master is Geryon, he tends to listen more to Eurytion as he actually cares about him. Similar to ancient myths, a powerful demigod, Percy, came to the ranch and killed Geryon, but unlike Hercules, spared Orthus as he did not participate in defending his master as Eurytion told him to stay back during the fighting between Percy and Geryon.

Trivia:
Geryon is featured in the 1981 film [| Clash of the Titans] serving as watchdog for Medusa's temple. Originally concieved as Cerberus, the third head was removed due to issues with budget and the construction of the puppet. In the film he is called Dioskilos.