It seems odd to me that so many people have commented on the slang meaning of "Fanny" without pointing out that the slang meaning in the UK (in use since about 1879) almost surely derives from a particular famous woman named Fanny, in this case the fictional Fanny Hill, chief character of Daniel Defoe's novel "Fanny Hill or Memoirs of a Woman of Pleasure" (1748), which was about a sex worker. The American slang meaning of "buttocks" does not occur before around 1920, and probably came about because American soldiers going to Europe in World War I heard British soldiers talking about women's "fannies" and did not quite understand the reference!