Tell them that their free trial is over and their company will no longer receive free trial keys. You can do that. It doesn't require a lawyer and it doesn't require threats. Just "We're glad you like our product! Unfortunately we can no longer support you with free trials." Be polite.
If they secretly keep getting free trials by pretending to be unaffiliated, then escalate to 1) blocking the fake ones when you discover them (very annoying to them, even if you don't get them all) and 2) as a very last resort, legal threats.
The goal is to get them onboarded as paying customers. Every other outcome is effectively a loss. You want to be polite but firm.
If it was me, I'd have- at the least - a little routine in the trial-signup logic on the backend which would check the company name and known aliases, and return "not eligible for free, but sales would love to talk! Have a nice day!" message.