Named after C. A. Kosberg - Soviet aeronaut (1903-1965).
Kosberg is a small lunar crater that is located near the middle of the huge walled plain Gagarin, which lies on the far side and cannot be viewed directly from the Earth. Kosberg is a flat-bottomed crater with a circular outer rim, simple sloping inner walls, and a somewhat hummocky interior floor. (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.