The OP's question was should the name/logo change.
If the society was called The London Folk Dance and Song Society then I wouldn't be having this discussion.
No mean spirited sniping intended indeed. I am looking at this from the perspective of a leader and manager who's likes to dabble at "Folk Music and Song" As opposed to A Musician/Dancer who likes to dabble in leadership and management.
Any organisation needs sound leadership and management, a credible vision and relevant objectives. It also has to live up to them.
I don't particularly care whether the EFDSS chnges its name to fit the aims and objectives, or whether it changes its aims and objectives to fit the name.
As an organisation though it must be responsive to change and the needs of its customers, therefore it has to examine itself regularly to ensure it is meeting it aims and objectives and its customers needs. If it doesn't then it will go under eventually.
Who Moved My Cheese