Named after Hervé-Auguste-Etienne-Albans Faye - French astronomer (1814-1902).
Faye is a heavily eroded lunar crater in the rugged southern highlands. It is attached to the northeastern rim of the crater Delaunay, with Donati located just a few kilometers to the northeast. It forms part of a chain of craters of increasing size to the southwest that continues with La Caille and ends with the walled plain Purbach. The rim is heavily damaged, particularly along the western half and covers much of the southwestern 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.