Named after Aristarchus - Greek astronomer (310-230 B.C. ?).
Aristarchus is considered the brightest of the large formations on the lunar surface, with an albedo nearly double that of most lunar features. The feature is bright enough to be visible to the naked eye, and is dazzling in a large telescope. It is also readily identified when most of the lunar surface is illuminated by earthshine. (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.