Named after Nathaniel Bowditch - American astronomer, mathematician (1773-1848).
Bowditch is a lunar crater that lies on the far side , just beyond the eastern limb. It is located on a region of the lunar surface that is brought into view due to libration, but at such times the area is viewed from the edge and so not much detail can be observed. It lies just to the north of the small Lacus Solitudinis lunar mare,. The rim of this crater is open to the southwest and the crater is elongated to the northeast, possibly due to a merged crater. (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.