Have you actually told her flat out what it's slang for? In many parts of the world, it is a perfectly normal name. And if English isn't her first language it might be hard for her to pick up on slang like that. Or she might nor care if you aren't actually living in an English-speaking country or planning to move to one, MANY names would become unusable if you considered what it would mean in other languages.

No "if"s, "and"s, or "butt"s?

Could be worse, I knew someone with the last name Hiney... could you just see... Fanny Hiney? :)

Tell her that Fanny means ****** and every time she calls "Come here, little Fanny!" she'll be calling "Come here, little ******!"

It is a decision that should be made by the both of you. Give her alternatives and grow some balls.

my ex is named Fanny. it is not a common name, but nothing to be ashamed of dude.

It means ****** down here in NZ. We have a French town here and it's the first I've heard of someone being called Fanny. OP change it to something else!!!! Use that name as her middle name

Call her ann for short. And sucks for you

Call her Francesca. Fanny for short.

You could look up a list of names on the Internet and show them to her. Uncommon or French or whatever kind of name you guys want and try to remind her this is your daughter too and you should both agree on her name or make some kind of compromise.