Deimos was discovered by Asaph Hall, III at the United States Naval Observatory in Washington, D.C. on 12 August 1877, at about 07:48 UTC (given in contemporary sources as "11 August 14:40" Washington Mean Time, using a pre-1925 astronomical convention of beginning a day at noon, so 12 hours must be added to get the actual local mean time).
Hall also discovered Phobos on 18 August 1877, at about 09:14 GMT, after deliberately searching for Martian moons.

It is named after Deimos, a figure representing dread in Greek mythology.
The names, at first spelled Phobus and Deimus, were suggested by Henry Madan (1838–1901), Science Master of Eton, from Book XV of the Iliad, where Ares (the Roman god Mars) summons Dread (Deimos) and Fear (Phobos).
Deimos was discovered by Asaph Hall, III at the United States Naval Observatory in Washington, D.C. on 12 August 1877, at about 07:48 UTC (given in contemporary sources as "11 August 14:40" Washington Mean Time, using a pre-1925 astronomical convention of beginning a day at noon, so 12 hours must be added to get the actual local mean time). Hall also discovered Phobos on 18 August 1877, at about 09:14 GMT, after deliberately searching for Martian moons.
It is named after Deimos, a figure representing dread in Greek mythology. The names, at first spelled Phobus and Deimus, were suggested by Henry Madan (1838–1901), Science Master of Eton, from Book XV of the Iliad, where Ares (the Roman god Mars) summons Dread (Deimos) and Fear (Phobos).
Deimos (moon)