The genus name Anurognathus is derived from the Greek αν/an- ("without"), оυρα/oura ("tail"), and γναθος/gnathos ("jaw") in reference to its unusually small tail relative to other rhamphorhynchoids pterosaurs. The species name A. ammoni honours the Bavarian geologist Ludwig von Ammon. Anurognathus was a member of the family or clade Anurognathidae.