The three-headed dog fought in the original God of War is Cerberus.
Cerberus is a monster from Greek mythology traditionally described as the guard dog of the Underworld. In the original God of War, Kratos encounters Cerberus as an enemy during his quest to defeat Ares. The game uses the familiar three-headed form, while also presenting related combat encounters involving Cerberus-like creatures.
Cerberus is sometimes confused with Orthrus, another two-headed canine in Greek mythology. Orthrus is associated with Geryon, whereas Cerberus is the more famous guardian of Hades. The God of War series adapts these mythological creatures for fast-paced combat rather than presenting them as strict historical or religious accounts.
The original game draws heavily on Greek mythological names, gods, monsters, and locations. Its myth-inspired setting is fictionalized, allowing the developers to connect separate legends into Kratos's revenge story.