Elfridia was named in 1985 by American paleontologist David Thayer based on material collected from Carboniferous exposures of the Swisshelm Mountains in Arizona. The genus name is derived from the nearby town of Elfridia, and the species name, E. bulbidens, is with respect to the bulbous teeth of the animal (bulbi- for 'bulbous' and -dens for 'tooth'). It is one of the oldest known 'microsaurs' and one of the few from the American southwest region.