Named after Cleostratus - Greek astronomer (unkn-c. 500 B.C.).
Cleostratus is a lunar crater near the northwest limb. It lies to the northeast of the crater Xenophanes, and west-southwest of the prominent Pythagoras. From the Earth this crater appears highly elongated due to foreshortening. The rim of this crater has become soft-shouldered due to steady impact erosion, and the formation is now just a depression in the surface surrounded by an eroded rise. (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.