Named after Christian Gärtner - German mineralogist, geologist (c. 1750-1813).
Gärtner is the lava-flooded remnant of a crater in the northeast part. It is located on the northern edge of the Mare Frigoris. The southern half of the formation is completely missing, and Gärtner forms a semi-circular basin along the edges of the lunar mare. To the north lies the crater Democritus. (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.