Named after Thomas Hornsby - British astronomer (1733-1810).
Hornsby is a tiny lunar crater in the western part of the Mare Serenitatis, a lunar mare in the northeast quadrant 's near side. To the north-northwest is Linné, a feature notable for its skirt of high-albedo material. To the west is the wrinkle ridge named Dorsum Von Cotta. (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.