The EU does recognize genericization of regional names in some cases, so I'm not sure it's in principle different from the U.S. on this, it just draws the line

The EU does recognize genericization of regional names in some cases, so I'm not sure it's in principle different from the U.S. on this, it just draws the line much further to one side, with a stronger presumption in favor of regional name protection. Two examples of regionally named cheeses now legally generic in the EU are "cheddar" and "emmental". These are the names of cheeses traditionally produced in the vicinity of Cheddar (in Somerset, England) and Emmental (in Bern, Switzerland), respectively, but have since become names for cheese style rather than cheese origin. There's an argument that "parmesan" should be similar, especially when used with a lowercase "p" in a manner analogous to the way "cheddar" is used, but the decision came out the other way on that one. One that's currently being litigated in the EU is whether labeling products not from Greece as "Greek yogurt" is misleading. I personally think yes, especially given the capital 'G' and the parallels with other clear origin-designating terms like "Greek wine" and "Greek olive oil" (and mixed origin/style terms like "Scotch whisky"), but it could end up going either way.