My BIL owned a few trucks recently and one of the runs they made was to Mexico to pick up Vidalia onions grown there. They were sold as Vidalias too.
The problem is that “Vidalia onion” has just became a generic name to describe a sweet onion, just as “bratwurst” has become a generic name to describe a particular type of sausage. So you can’t really go and retroactively reclaim the name.
Wisconsin cheeses is pretty general; for example, a Wisconsin cheddar or a Wisconsin blue means that they’re from Wisconsin, but the cheddar or blue describes the type of cheese. Maybe the Europeans should just go for inserting the word “true” or even their country name before the regional name that has now become a generic description: “True Brie,” or “French Brie,” for example, instead of trying to get the rest of the world to retro-adapt to their demands.
And Vidalia onions from Vidalia could be called something like “Georgia Vidalias.”
My guess is that if you looked at the name closely it would say “Vidalia-like”....with Vidalia very pronounced and the “like” much smaller.
When I’ve bought them, they were labeled Mexican Sweet Onions or just Sweet Onions. And they aren’t as sweet as Vidalias.