Interested in Language
I would like to know if it's correct to use ingame.
My name is Nightmare in this game.
My ingame name is Nightmare.
I will send him a message in game.
I will send him an ingame message.
All advertisements in game are annoying.
All ingame advertisements are annoying.
As you can see, I only use ingame when it's directly linked to another word.
Is this correct?
It depends what you mean by 'correct'! I've certainly met 'ingame', and its meaning is clear (though a hyphen would help). It's certainly not a formally recognized word.
Of your six sentences, the last four make more sense to me than the first two. In that case I'd spell out 'my name in the game...', or use a word recognized in the online world, like 'monicker' or 'handle' (again, these aren't formal).