You can definitely make a game about a real serial killer that’s surrounded by theories, myths, or popular portrayals, that’s totally fine. As long as the core of your game is still grounded in a real person and real events, you’re good.
It doesn’t have to be strictly limited to only verified facts. A great example is the Zodiac Killer, his full identity was never confirmed, the crimes themselves are very real, and a lot of stories build on theories or interpretations around them.
Just make sure the project isn’t completely fabricated. The real-life inspiration should still be clear and recognizable,(aka with one google search I can see who you based the game on)