I think it’s Garry’s Mod because it’s Garry’s modification of the source engine. Hence the name, Garry’s Mod.
The point of the game before was just a simple sandbox game where you would put Alyx in random sexposes with a giant Antlion. The game evolved into the point where it was so modifiable that you could have Alyx in random sex poses with 10 giant Antlions while shooting cats out of her eyes.
If the name was to imply that the “fucking game” was to mod and hack then it would simply be called, Garry’s Sticking Shit Up Alyx’s Minge Mod.