Aus. tends more to the British style in language so I feel I can answer to some extent.
I've never heard anyone hedge around saying "Fanny" as a name, but then saying "fanny" as a body part isn't the catastrophe that it seems to be in the US.
We all manage OK with faggot - which is bread, or old fashioned firewood.
" " fag, which is a cigarette.
" " rubber, which you would call an eraser.
There are bunches of them. It would be interesting to make a list of transAtlantic differences in meaning..
Let's face it, English has so many words with multiple meanings, even diametrically opposite meanings, that we are all used to considering context
Fanny as a body part is not a catastrophe in the United States. My own grandmother and mother and even my dear and devout Southern Baptist Aunt Mary used this term in relationship to what might happen to the bottoms of small children if they didn't stop (doing whatever). Frequently. If any of the kids used it, it wasn't even a raised eyebrow but we did not dare use the word 'butt' unless we were talking about leftover bits of a cigarette. Bottom was acceptable.
Fag as cigarette seems to have gone out of fashion somewhere in the 50's or perhaps early 60's. I only remember reading about it, not ever actually hearing it. As a pejorative for homosexuals: very common place when I was young (and considered worthy of a slap in the face if heard by an adult) but never actually spoken by an adult that I heard, less because it wasn't considered to be polite language than it was thought to not be polite to discuss the possibility of homosexuality, but haven't heard it in a couple of decades, at least. Faggot as firewood is almost unheard of except as an obscure literary reference. The kids (40's and younger) these days don't see anything pejorative about being gay, lesbian, bisexual, transgender, queer, questioning, etc.
Rubber = condom at least by the 70's. Caused an outburst of laughter during the high school staging of Our Town when Tom was urged to wear protective footwear in the rain.
I remember my mother telling us to wear our rubber boots, although they surely were made of something cheaper and less sturdy than actual rubber.
Richard is a name that is uncommon among the under 50 set, and most men I know with that name use Richard or Rich or maybe Ricky rather than Dick. The name was out of contention when naming our own children, as was the name Peter.
I cannot say that I've ever known anyone named Fanny but it doesn't cause any raised eyebrows. I have a Fanny Farmer cookbook and even my sons never raised an eyebrow or made a snide comment.
