Hellhounds are monsters found in Doom RPG (a member of the Canine class) and Doom Eternal (as a creature summoned by Marauders).
Background
Doom RPG
The Hellhound is a monster found in Doom RPG belonging to a demonic class known as Canines. Hellhounds are brown members of the species. They can be captured with dog collars to become a trained attack dog.
Doom 3
The Pinkies in Doom 3 are also referred to as 'hellhounds'.
Doom Eternal
The Marauder will occasionally summon an orange spectral Hellhound, which chases you and delivers biting damage. While more of a nuisance than a threat, damage from the Hellhound can add up quickly and distract you from the fight at hand.
Behind the scenes
A sculpture of the Hellhound by Gregor Punchatz.
The Hellhound is a monster intended to appear in Doom 64, and sadly, it didn't make it to the final cut. Its existing sculpture is that of a demonic canine with two heads, resembling the Greek mythogical Orthrus.