Named after Sergey Konstantinovich Kostinskiy - Soviet astronomer (1867-1936).
Kostinsky is a lunar crater on the far side. It is nearly attached to the northeastern outer rim of the crater Guyot. About one crater diameter to the southeast is Ostwald, and farther to the north is Olcott. The rim of Kostinsky is eroded, and along the southeast has been nearly worn away. (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.