Named after Demonax - Greek philosopher (fl. 2nd century A.D.).
Demonax is a lunar impact crater near the southern limb. This location makes the crater difficult to observe due to foreshortening. The crater is also illuminated at a very low angle, when it is in the sunlit side. Demonax lies just to the north of the crater Scott, one of the south polar formations. (wikipedia entry)
A crater is a circular depression likely created by an impact event. On the Moon they are named after deceased scientists, polar explorers, astronauts or cosmonauts.