I want to add in my game some Dungeons'n'Dragons monsters (like Mindflayers, Gnolls, Sahuagins and Beholders). But my game is free: you don't need to pay for playing it. Do I have to pay copyright?
If those monsters are trademarked by Wizards of the Coast (and I think they are), then yes, they might come after you to pay royalties. It doesn't matter that your game is free; you'd be using someone else's intellectual property. That's unfair and nonsensical, but sadly it's how the law works in most countries nowadays. At least file off the serial numbers. Name them something else and change some cosmetic details. It's how they derived halflings from hobbits originally after all.
Only a handful of D&D monsters are original creations. Much like Disney, most of their characters are "borrowed" from various myths around the world. If you're in doubt, just Google the monster's name. If there's any tradition, then you're in the clear. If the only Google result is D&D, then you're not.
Beholders were specifically designed for DnD, so they can be used by Wizards of the Coast to bully you (no, they are not fighting copyright infringement. They are just bullying you, however the law backs them up, showing that justice is not always just). Same goes for gnolls and Sahuagin, and I couldn't even bother anymore to look up the Mind Flayer (which I did also find in Final Fantasy I (for PlayStation), under a different name, but I guess that's rather a miss-translation than a copyright issue avoidance).
Like MaxSMoke777 said, the majority of the monsters you'll find in the monsters manual for DnD (any edition) are directly copied from folklore and mythology and some of them even from religions that still have followers today (like Tarasque, which came from a French Christian legend). Trolls regenerating can be a hard one.
Trolls themselves are in the public domain due to being part of age old folklore. I looked them up, but could not find mention of regenerating properties. Now I did also find Trolls in the Wild Arms series, who have a free healing action at the end of every turn in combat, which makes me think that was heavily inspired on the regeneration properties the DnD-variant is famous for, and I doubt Wizards of the Coast were ever paid royalties for the examples I just named.