It was apparently his old dog, because now he has Ushnar's Dog. The Skinned Hound will be reanimated after the completion of the quest Ushnar's Terror (a quest unavailable to Khajiit players, as the Orc is afraid of cats) and will follow the Hero until death. It's not possible to tell the Skinned Hound to wait, and it won't respawn.
If the Hero fast travels, the Hound doesn't travel along. Instead, its Speed is temporarily increased to 255 to catch up with the Hero.