What I meant was I never heard it in the context being discussed now, as a substitute for the posterior. However, I am sure it is the diminutive for Frances.
I am confused now. It is OK to call somebody Fanny if it is her name, but to call someone that if it is NOT their name is rude. 
I assume her name is Fanny? In which case, no - because it her name, and doesn't refer to a lady part.

