Deimos

Deimos is the smaller and outermost of the two moons of the planet Mars, the other being Phobos. It is the scene of the second Doom episode, The Shores of Hell. Deimos is named for the Greek god of dread and terror, and a son of Ares.

Doom Classic
According to the Doom Manual, Deimos is used to store nuclear waste, and is also the home of teleportation experimentation with Phobos. Sometime before the game however, an experiment goes wrong, Deimos vanishes, and the Phobos base is attacked by an unknown force, and the player's squad is sent up to investigate.

By the time the Lone Marine crossed over to Deimos, he found the human personnel there slain or transformed into zombies, and the complex was now under the command of a Cyberdemon and its minions, who were gradually transforming the advanced facilities built there by humans into a grim bastion of great evil. However, the Marine was able to battle his way to the Cyberdemon's lair at the Tower of Babel, and destroyed its infernal master, avenging the loss of human life on the moon station.

Doom 64
Deimos appears to be indirectly mentioned in the manual for Doom 64. Interestingly the choice of words the manual uses seems to imply that Deimos has somehow returned to its orbit around Mars (it mentions 'installations' plural presumably Phobos and Deimos, Our Hero believed he had cleaned up previously during his 'first mission' during the classified "Doom episodes'..). There are also levels that could possibly take place on Deimos, Phobos, and/or Mars Base ("planetary" is mentioned twice).

However, the levels may actually take place on Mars, as the second level is a terraforming installation, it is unlikely that either moon could be terrafored as there is not enough rock to hold an atmosphere. The reference to 'first mission' still works however, as Hero was stationed on Mars, before he traveled to the moons. Also the manual for Doom II, establishes that the Marine (Doom II) fought demons on Mars before escaping back to earth.

The background to the level as seen in Terraforming level shows mostly stars, but once you reaching the terraformer, you can make out reddish-brown cliffs. These might somewhat resemble Deimos's somewhat 'snowy' crags seen in Shores of Hell, but could easily respresent Mars as well.

Doom RPG
Deimos isn't shown physically in the fly-in in the intro, however its orbiting projection is shown under Phobos.

Doom (2916)/Eternal
In 2016's DOOM Deimos and Phobos are used as mining stations, although it is never stated, or implied that any outbreaks, or military operations occurred there.

Behind the Scenes
In Doom Deimos is represented as having older style bases (barring the presence of Hell corruption) composed of Brick, and Cement walls, the shape of the Deimos is notably square compared to the abstract-design of the Phobos, and Inferno levels. Deimos is also represented as having large brown mountains capped with small amounts of snow, despite the intermission screen showing a grey landscape, similar to how Phobos is shown having large grey mountains covered in vegetation, but a brown cratered landscape in the intermission screen, and in levels.

In reality, Deimos is much smaller than Phobos, only having a radius of 6.2 kilometers, possess little gravity, and no atmosphere (even if it had an atmosphere, it would drift off without some form of Artificial Gravity technology).