I think that nuance is significant. Does it see its purpose as promoting English folk music, ie the folk tradition native to England, or is it trying to stake a claim to all folk music performed in England, from any culture or background?

Both are respectable objectives. Its charitable objects include "to preserve English folk dances and songs and other folk music" When you look at what we mean by "Irish folk music" or "Scottish folk music" it seems reasonable to interpret "English folk music" to mean the native folk traditions of England. (I realise that no tradition exists in isolation, so let's not get diverted by what is "English folk music", you know what I mean).

The inclusion of "other folk music" allows it to extend its scope beyond this. However I wonder how some other communities might feel about EFDSS/Folk Arts England claiming to represent their music?

This is all part of what I mean about deciding on a direction before choosing a name. Of course a name can't encapsulate everything, but it should try to convey its main activities.

I fear FARTS may stick, no matter how hard they try to insist on another abbreviation. DEAFASS (the Dance Earnestly and Forget About Song Society) is still about more than 40 years after Lawrence Heath coined it, and long after it ceased to be a fair criticism. Remember that the majority of folkies are not members, find it of little relevance to them, and are very ready to find fault.