Yes, it is a real name. I've never seen it spelt like that, but my great grandmother's name was Fanny. I suggest not naming your kid this because of the teasing that would likely come with it.
A lot of parents feel the need to "vary" the spelling of their children's name to make the name "unique." I think it's awful. Imagine your name being spelt wrong all the time! Everyone always spelt my name wrong and it's VERY annoying.