When a person signs up to a website they can use any false name they want that is not their real name and they can use a throw-away email that was also signed up under a false name.
So the website can say under court order that the name that was used at signup is “Barack O’Blahblah” who lives at “1600 Cesspool Lane”. What good is that going to do the plaintiff?
If the plaintiff tries to shut down the website for slander, that will be difficult as the website can counter that their first amendment rights have been violated.
The union thug could have the website operators stalked and threatened and that could cause website to ban the offensive poster. But that would be coercion and union thugs never use coercion do they?
They get the IP address and use it to identify the person responsible. Even behind a proxy, they can still track you down. See: Kernell, David.
“What good is that going to do the plaintiff?”
You can call yourself anything, but the ISP has your address, 186.111.222.123. How many times have you gone to a website in Timbucktu and seen advertisements from your local Sears? That’s because the ISP knows exactly where 186.111.222.123 is, right down to your street address.
Unless you are using Tor or some other proxy, they know your IP address. That's all they need.