As for "bourbon", has anyone claimed the rights to that yet? I know that scotch is only allowed to be explicitly labelled as such if it is distilled in Scotland; has the US (or even a region in the US associated with bourbon such as Tennessee) attempted to have bourbon classified in a similar manner?
The protection of designations of geographic origin is a global hodgepodge of local laws combined with international treaties like TRIPS, with disputes being resolved in an arbitrary manner before a number of bodies and courts completely dependent on who is being sued where, about what, and what is being claimed.
Also lots of things get grandfathered in even after agreements have been reached on general subjects. For instance, "Champagne" is one of the most obvious geographic origins, where the mere word indicates a sparkling wine of certain qualities from the Champagne region of France.
Yet, despite this, you see "California champagne." Without that additional qualifier, this would be illegal in most places in the world.
Then, there are worse offenses (I say worse because California champagnes do not generally insult the quality of the regional wine). For instance, Kraft's Parmesan cheese, which is absolutely awful garbage. It is, in fact, actually illegal for them to call this Parmesan or even imply it is related to Parmigiano-Reggiano or other protected designations of origin. In Europe, they have to sell it under the ludicrous appellation "Pamesello Italiano," although, frankly, I think it should be illegal even to call this cheese anywhere.
Bourbon is defined in the United States as such:
en.wikipedia.org
There's just too much to paste there. An interesting one is the bottled-in-bond variety which is one of the more stringent to qualify for legally but yet weirdly underrated. This subvariety is particularly bizarre because of the absolute requirement of federal government involvement to be called this.
Needless to say, the rest of the world could give a shit less about the utterly weird and nearly incomprehensible American rules on this, hence Japanese bourbon-styles, under whatever names.
The general rule, where there isn't a more specific rule, is that if a name necessarily implies that something is from a certain location or made in a certain way, it is illegal to present a product as if it comes from that place and/or has those qualities.
So for instance, "Virginia ham" or "Idaho potatoes" mean that the products in question actually do come from Virginia or Idaho. Bourbon may have specifically American definitions that apply here, but the rest of the world doesn't necessarily respect those local rules. Someone selling "Virginia ham" in some European country where people with an interest in selling actual ham from Virginia, though, would be looking at a lawsuit. Whether that would be local or before some WTO body would depend on who was doing the suing and why.
For instance, some things (Virginia ham is definitely one of these) are big enough that you, the corporation selling Virginia ham, might literally get Virginia itself or even the United States to do the suing and before a TRIPS body to make it an international incident.
This might also happen if you had some foreign company trying to sell "Kentucky straight bourbon whiskey." Just the word "bourbon" is a little shakier, though.