Named after Charles Darwin - British natural scientist (1809-1882).
There is a Darwin crater on the moon and a suspected crater named Darwin on Earth. The crater's name was formally approved by the IAU in 1973. To the northeast are the craters Green and Roddenberry. (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.