Risso's Dolphin was first described by Cuvier in 1812. Another common name for Risso's Dolphin is the Grampus (also the species genus) - although as a common name was historically used to describe the Orca. The etymology of the word grampus is unclear. It may be an aglomeration of the Latin grandis piscis or French grand poisson both meaning big fish. The specific name griseus refers to the mottled (almost scarred) grey colour of the dolphin's body.

It is found worldwide in temperate and tropical waters, usually in deep waters rather than close to land. As well as the tropical parts of the Indian, Pacific and Atlantic Oceans, Risso's are also found in the Mediterranean and Red Seas, though are absent from the Black Sea. Their preferred environment is just off the continental shelf on steep banks (with water depths varying from 400-1000m) with water temperature at least 10° C and preferably in excess of 15° C.