Richard Mabey in Flora Britannica under Anthriscus sylvestris lists
Queen Anne's Lace, Fairy lace, Spanish lace. Kex, kecksie, Queque, Mother die, Step mother, Grandpas's pepper, Hedge parsley, Badman's oatmeal, Blackman's tobacco and rabbit meat Not a bad collection.
Daucus carota just gets wild carrot and bird's nest.
I don't think you can have a right and wrong in common names. If it's what people call them it's the common name.
Yes, if that's what people use then that's the name. However, if a 20% of people mean carrot, 20% of people mean cow parsley, 20% mean Bishop's Weed, 20% mean Hemlock and the other 20% mean any umbell then telling some Queen Anne's lace can be good to eat could get you into trouble. Common names are therefore pretty meaningless. But you can call it whatever you like.
In Yorkshire, yer kecks are yer trousers. And yer bannickers are yer overalls.
In Lancashire too. And Pants are Trousers and Troose are 'ladies Trousers' And you don't get snowed under with work you get snood under in my family.