Yep, I also thought 'squaw' means Native American wife. At least that's what they say in Western comics :-) But then again, comics give such a destorted view on Native American tribes anyway; I can't believe they have survived and still get published to a wide audience in the 21st century!
Fanny and Fanni have been all the rage here in Finland as well, since the early 1990s. The name became popular together with other old-fashioned, cute names such as Ida, Emma and Sofia. I believe Fanny even made it to the Top 10 at some point. By now people are getting tired of these overused names and are turning to something else instead, so the popularity of Fanny is dropping rapidly.
The connection to arse or vagina is unknown of, unless you happen to be an English scholar or otherwise love leafing through dictionaries :-)