Is it illegal to mention words like batman, Netflix or iPhone in my game?
They are trademarks, so strictly speaking you can't use them without authorization.
As
GNVE implied, in daily and private use, it doesn't matters this much. But here it's a public use, and potentially in top of this a commercial use.
Most of the time, rights owners wouldn't care this much about an indie game with a small audience. But here it's adult content, something that not all brand want to be associated with. And there's also the case of companies like Apple, who really care about their image. By example, Apple strictly forbid that their products appear in the hands of bad guys, or that those bad guys name them ; pro tip, if in a movie everyone own an iPhone except one guy that feel odd, your guts are right, it's the traitor.
I have played some games where developer changed the names to like 'netflux' or 'betflix'
Because there's an unwritten rule:
Better looks a bit ridiculous, than take the risk to have an international lawsuit in the ass, and face millions dollars lawyers with my two bucks lawyer that will shit his pant before he even have the possibility to say a word.
Strictly speaking, the risk that someone sue you is really low. At most they'll firmly ask you to stop, and you'll nicely comply, hoping to never ever hear about them again.
But there's still this 0,0001% risk that a right owner was in a really bad mood when he heard about your game, and it's a risk that really few a ready to take. Even if you win the case, it mean years of procedure, tons of money spent in advice and legal representation, and a constant level of stress that you probably never faced before. Level of stress due to the fact that if you don't win, in top of what you already owe to your lawyer you'll probably have to pay more than what you earn early at your current job.