It doesn't work in the US, and I'm assuming not in the UK, either. Although the slang term "fanny" doesn't have the same meaning in the two countries, it denotes a nether region in both.
I had a friend in middle school named
Fanny. She had moved to the US from Uruguay, where I presume
Fanny is fine. She found it necessary, after a few years, to start going by her middle name,
Renee.
I can't really put myself in a time, though I know such a time existed, in which the word "fanny" does not mean "rear end", so that colors my perception of the name to the point that I can't judge it on its own merits.