The information I have says that Fanny (Frances) Power was the daughter of David Power of Coorheen. She married Richard Trench of Garbally in 1732, and some copies of the tune were called "Mrs. Trench". In the words accompanying the tune (which I unfortunately don't have), I understand that Carolan says he hopes to live to dance at her wedding.

That would make them Dick and Fanny Trench - even more smutty inuendo!!

Interesting that in the US, the fanny is the back bottom, and in the UK it's the front bottom...... wonder which one was first?

LTS