A dogfish is a kind of small shark, not a fish that is a dog, and not usually the big movie sharks people picture. Several related sharks get this name; they are often grey-brown, stay near the bottom or the coast, and are much smaller than the famous hunters. English named them dog + fish, and a lot of other languages made the same picture — “dog of the sea,” “sea-dog,” “little dog” — probably because of the snout, the way they hunt, or an old habit of calling some sea animals after dogs. In shops the meat has sometimes been sold under a nicer name, so a diner might eat dogfish without seeing the word shark. Informal everyday English for the animal; a bit specialist if you are naming the exact kind.