how exactly will consumers be able to sue any given establishment?
Private courts. Will that business just be able to ignore the ruling? Sure, but it will make life difficult for them. Would you do business with a company that has a history of never allowing itself to be brought to justice? Probably not.
Who chooses which private court? Presumably there will be many, each catering to different markets for justice, and even some competing in the same market.
exactly why any given restaurant cannot declare itself to be the "real" burger king?
Let's say my name is Bill Gates and I sell software "made by Bill Gates". Of course I can slap my name on it. Of course I can claim I'm "the real" Bill Gates. What I can't do is intentionally lead anyone to believe that I'm "that other" Bill Gates. That's fraud, pure and simple.
It might be difficult for any random guy called Bill Gates to pretend to be the Microsoft (TM) guy - a small matter of not having an enormous personal fortune at hand. But
who can stop me opening a restaurant called "Burger King", with the same sign over the door, the same color seats, the same menu, the same everything - except (maybe) the food? Likewise, the website catering to NineInchNails - who can stop me setting up a website claiming to be the "real" site that sends contributions to the musicians, even with a nice video (suitably 'shopped) from the lead singer? If you answer to this latter is TOR, cryptography, etc, then you'll be waiting a long time for Joe Public to figure it out. Bitcoiners are savvy, but it's clear bitcoins ain't never going mainstream for exactly this reason.