The phrase "Dungeon Master" is a registered trademark[1] by the rights holders of Dungeons and Dragons. DM is the abbreviation of that, and most likely safe to use. Game Master (GM) is used as a generic (and game agnostic) term.

[1] https://trademarks.justia.com/742/64/dungeon-74264094.html

Edit: I have (twice) edited this now after additional information from others (thank you Kichae for the link to the Dungeon Master trademark) was posted on this thread.