Named after Pierre Puiseux - French astronomer (1855-1928).
Puiseux is the remnant of a lunar crater that has been almost completely submerged by lava. It is located near the southern end of Mare Humorum, to the north east of the ruined crater Doppelmayer. To the south-southeast is Vitello. Of the original structure , only the upper part of the rim remains above the mare surface. (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.