San Marzanos are origin-protected in Italy, so if you get Italian San Marzano's they're legally limited in ways that promote quality.
Unfortunately, there is a large black market in mis-labeled San Marzanos, so it's not a full guarantee of quality. But it's something that they're at least working on, rather than just giving up.
"only this company can decide who can use the trademark"
It's like:
"only if it's production fulfills certain criteria can you use the name"
It's made as a consumer protection so that people can not just claim their product is this kind of "traditional" product when it isn't. Except that it's less used like a consumer protection as it's mainly used like a trademark. Controlled by a small group of people and directly profiting some regional government/economy.
Most commonly it requires the main ingredient to come from a specific region (also e.g. used for Wine or Sect).
EDIT: I kinda did throw different regulations into one explanation here.
Cheddar in most places outside the UK is "not cheddar". If I go to the supermarket here in Sweden and buy the first "cheddar" I see prominently displayed, I'm not getting cheddar from the UK.
I will have to try it next time over there, but please don't be offended when I say that based upon all the cheeses I have eaten over there I won't be holding my breath.
You know how "champagne" is technically only champagne if the grapes are from the Champagne region of France, and otherwise it's just sparkling wine? That's a legal designation in the EU.
> French producers are still allowed to use the word champagne on the front of bottles, but the use of "shampanskoye" is allowed only on local produce.
The EU is the main place that has these laws sorts of laws. I beleive that they will include it in trade deals so that it is enforceable in more of the world.
I may be wrong but I believe the canada-eu and eu-japan treaties also protect most denominations of origin (or rather, most by value rather than by specific items, but San Marzano should be included).
It's a regulation [0] that says that products that are associated with a specific geographic location cannot be manufactured elsewhere and then passed off as the original.