John knows one thing, a name. Simple as that.

Explain how you can frame an organization that is unknown. Explain how you can make them look bad if you are the primary target. Explain how to get people to look for them when they are looking for you. Go ahead and use their name, the only thing you would be doing is helping them stay hidden because its you, what happens when you get caught? Are you going to tell them it was the complex and not you? That would make Dark matter look like an idiot. So go ahead and use their name, they won't go after you simply because that would be foolish. The biggest threat to you would be yourself. Dark matter would only be setting himself up.