Named after Gaspard Monge - French mathematician (1746-1818).
Monge is a lunar crater that lies along the southwestern edge of the Mare Fecunditatis. The interior floor is somewhat irregular in the eastern half, and there are accumulations along the bases of the sloping interior walls. The nearest named crater is Cook to the northeast, while the larger Santbech is located to the west-southwest. (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.