Named after Cristobal Acosta - Portuguese doctor, natural historian (1515-1580).
Acosta is a small lunar impact crater located just to the north of the prominent crater Langrenus, near the east edge of Mare Fecunditatis. To the west are the trio of Atwood, Naonobu, and Bilharz. The crater is circular and bowl-shaped, with a small interior floor at the midpoint of the sloping inner walls. (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.