Satan

Satan is a leader of Hell. Satan doesn't give second chances, and neither do his playmates.

Ingame sightings
The name Satan Appears in the ending of Classic DooM's 5th Episode: Sigil, Where It is explained Satan had bade Baphomet to bring Doomguy back to hell without realising that doomguy was the reason the invasion on Mars failed.

" Baphomet was only doing Satan's bidding by bringing you back to Hell. Somehow they didn't understand that you're the reason they failed in the first place. 

''After mopping up the place with your arsenal, you're ready to face the more advanced demons that were sent to Earth. ''

''Lock and load.  Rip and tear. "''

Besides this mention, the bosses for sigil are a Spider Mastermind followed by a cyberdemon. Satan,called by this name, never appeared in the game. leading some beliefs Satan and the Icon of Sin to be the same entity in the classic DooM, but that is not confirmed.

In the 2016's reboot of the game It is established that the Icon of Sin is the demonization of the betrayer's resurrected son. Thus hinting that he and Satan are probably different entities.

In DooM 2 ingame, DooM 3 and DOOM (2016) "Satan" is not mentioned.