Every language can have as many names as it’s needed and they can be set to certain geography, you can check it as anyone can add them.
You still can gather that info using fields and description, some varieties are added (though I don’t really remember seeing plant ones), but they’re taken very differently around the world, can have different names and uncertain genetics, it’s too much of a mess to add and control for curators who already have a lot of work to do. Check https://forum.inaturalist.org/t/where-to-store-plant-variety-information/4444
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