Now that's a good question! The answer is probably.
If you drop the English as Suibhne suggests that would make it more Cosmopolitan.
That leaves the "Folk Dance and Song Society". However there are those who might wish it otherwise such as the "Folk Song and Dance Society"
To avoid argument drop the Dance and Song which leaves "The Folk Society" However this is less descriptive of the work done so why not add Heritage to Make it the "Folk Heritage Society".
Anyway, I suppose if you did so, then the leading lumieres of EFDSS as it stands at the present would probably go into a song and dance about it!!!!
Neither a wise man nor a brave man lies down on the tracks of history to wait for the train of the future to run over him. ~ Dwight D. Eisenhower