Phobos (moon)

Phobos is the larger and innermost of the two moons of the planet Mars, the second being Deimos. It is the scene of the first Doom episode, Knee-Deep in the Dead. "Phobos" is Greek for "fear".

Background
According to the Doom Manual, Phobos is used to store nuclear waste, and is also the home of Teleportation experimentation with Deimos. Sometime before the game however, an experiment goes wrong, Deimos disappears from sight, the Phobos base is attacked by an unknown force, and the player's squad is sent up to investigate. The squad ends up being defeated sometime later, and the Lone Survivor ventures into the base, eventually defeating the Bruiser Brothers and supposedly dying after being teleported.

In Doom RPG, the moon Phobos is seen when the Doom Marine (B.J. Blazkowicz III) is seen landing at the old Mars Outpost (Mars Research Facility). (Deimos on the other hand is missing likely a nod to events of the original Doom)

Quake Arena/Champions
The moon Phobos is also mentioned in the back story for Doom (character) and Phobos (character) in Quake III Arena, and Quake Live..

Behind the scenes
In Doom, Phobos is depicted with Earth-like gravity, a thick atmosphere, and tall, seemingly vegetation-covered mountains; the sky texture for the episode was derived from a photograph taken of Yangshuo Cavern in China. However the map of the base shows that there is no vegetation and its set in a crater.

In reality, Phobos is a asteroid, some 20 kilometers in diameter with gravity less than a thousandth of that on Earth, and no atmosphere (even if an atmosphere could be generated artificially, the moon's gravity would be insufficient to hold it in place without its own artificial gravity). To be more plausible, future releases (Doom 3, and the 2016 reboot) moved the plot to Mars.

Phobos and its base are mentioned in Doom (2016), and is set to return in Doom Eternal.

However, while the character can seemingly walk around outside the base's buildings in some maps. It is known that the character is generally portrayed as wearing a breathing mask as seen in the box art (which may allow/protect him from the low-atmosphere of the moon).

In Doom 64 backstory it mentions that a 'planetary' base was sealed, and bombarded with "apocalyptic amounts of radiation" which allows the Mother Demon in a crippled state to resurrect the dead demons, a nearby satellite detects this and in a dying message relays this back to Earth, and the Doom Marine is sent back to this facility defeat the demons. Some interpret this facility be Phobos although the reference to 'planetary' (twice) could also be a reference to the UAC Mars Base from Doom II backstory which a Marine stopped an invasion (perhaps forshadowing or mirroring the events of Doom 3 or Doom RPG).