1. While you generally cannot trademark a geographic city name, you can trademark a distinctive style of writing that name. Every sports team and College or University does it in some form or another, like an interlocking LA or NY or old Boston B or the style of print. And you want that to be the case, or else the market would be even more flooded than it already is with crappy knock-offs of the trademark.
2. The Dodgers use the Brooklyn mark extensively in commerce. Look at the Cooperstown Collection apparel. Someone posted that they should be forced to use it on the field. They have, repeatedly, including at Old Timers functions and Hall of Fame games. One of the reasons many sports teams have been using flashback or throwback uniforms (like the Jets using Titans stuff) is to establish that they still use their old trademarks.
3. Why do you think the burger place used the distinctive Brooklyn script? Because they want to specifically reference and enjoy the benefit of all the good will the baseball team generated with that logo. That is not right. The Dodgers have invested a ton of money generating that. Shouldn't they be entitled to protect it? The burger joint is free to use another print style and create its own good will; don't try to take a free ride on someone else's.
4. Someone posted that Baseball should license the burger joint to use the logo. How do you know that they haven't made that offer? That is common in circumstances like this. Maybe the burger joint rejected it? Or refused to maintain certain quality standards, or not sell t-shirts that with the Brooklyn script, etc., etc. Don't jump on the team unless you know the entire background.
5. Trademark holders are forced to take action when someone tries to trademark a similar logo. If they let everyone use the trademark and did not police and protect it, you would jump on them for not taking sufficient steps to keep it disinctive (and the law would agree with you). You can't have it both ways -- criticize them for not protecting it and then criticize them for protecting it. Nor can they wait. What if the burger joint is successful and opens another and then another and then another burger joint, and then the Dodgers take action. Then you would argue that they slept on their rights and it isn't fair to the burger joint because they have now invested in building a name and market using the name.
6. The decision in the prior lawsuit involving MLB and the Brooklyn Dodgers logo linked to above was VACATED by the court, meaning that it was withdrawn, is not binding, and has no value as precedent.
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