Risso's dolphin is named after Antoine Risso, whose description formed the basis of the first public description of the animal, by Georges Cuvier, in 1812. Another common name for the Risso's dolphin is grampus (also the species' genus), although this common name was more often used for the orca. The etymology of the word "grampus" is unclear. It may be an agglomeration of the Latin grandis piscis or French grand poisson, both meaning big fish. The specific epithet griseusrefers to the mottled (almost scarred) grey colour of its body.
Infants are dorsally grey to brown and ventrally cream-colored, with a white anchor-shaped area between the pectorals and around the mouth. In older calves, the nonwhite areas darken to nearly black, and then lighten (except for the always dark dorsal fin). Linear scars mostly from social interaction eventually cover the bulk of the body. Older individuals appear mostly white. Most individuals have two to seven pairs of teeth, all in the lower jaw.