> 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

The geology-centered conception of terroir in wine that you're giving is actually rather controversial and not generally supported by any science we've done to date.

For wine, "terroir" rather encompasses things like climate, local customs and practices (viticulture and vinification), and sometimes things like local strains of grapes or of yeast.