Yeah the gills always seemed like a very loose categorisation, probably mostly as a precaution for poisonous species found in eastern european forests. I have to say I wouldn't be 100% comfortable implementing a feature like that not being an expert, especially with how many mushroom books are being reported with wrong information. It would be fun to have a small quirk for every forage type though.
As for the names, I'm pretty well aware of e.g. fly agaric and death cap being the poisonous mushrooms™, however I was not familiar with their english names before looking into the subject, even though I'm pretty fluent and I play in default language. Just in case anyone was interested in some feedback from a non native.
So basically weed need a champion like Gneiss, just for mushrooms. Hit us up, we're a loyal fanbase.