There are a lot of food and drink items with official legal definitions that include the region of origin. The most famous one is champagne, which can only be called champagne if it comes from a specific region.

You can think of the name as being inclusive of the region, not simply descriptive of the variety. So if someone made a sparkling wine in a different region and sold it as champagne then they would be committing fraud.

> Like if I plant some in my yard and start selling them online or at the local farmers market, what is anyone really going to do?

At your farmer’s market? Probably nothing. But if you came across a particularly grumpy person with time and money to burn on lawyers they would have a case against you. Not actually going to happen at that scale. But if you owned vidaliaonions.com and started selling fraudulent vidalia onions at scale, the farmers would likely get together and pursue legal action to protect their prices.

It’s almost like a brand. You can sell LEGO-style bricks but you can’t call them LEGO because they didn’t come from the LEGO company.

> You can think of the name as being inclusive of the region, not simply descriptive of the variety.

The term of art is terroir [1], which is the "character" of the environment the plants are grown in. It's often that a region will have some special characteristic due to geology that allows a unique flavor profile to grow so these trade names are the equivalent of a terroir brand.

Some designations are more strict than others, though. IIRC in the case of Vidalia onions the soil is low in sulfur so the biochemical pathways in onions that produce astringent compounds are nutrient starved. As far as I know most sweet onion varieties nowadays are grown in similar soil, but they're not legally allowed to call them Vidalias.

[1] https://en.wikipedia.org/wiki/Terroir