Named after Asaph Hall - American astronomer, discoverer of Phobos and Deimos (1829-1907).
A crater is a circular depression likely created by an impact event. On Phobos they are named after deceased scientists involved with the discovery, dynamics, or properties of the martian satellites, and people and places from Jonathan Swift's "Gulliver's Travels".
Image Source. Marker locations are approximate and may not always appear to align with image on map.