Fannie is the English diminutive of Frances — from the Latin francus (free, Frankish). Fannie Lou Hamer (1917-1977) — African American civil rights organizer; her 1964 testimony before the Democratic National Convention Credentials Committee in Atlantic City — including the account of her brutal beating in the Winona, Mississippi jail in 1963 — was so devastating that President Lyndon Johnson called an impromptu press conference to take her off live television.
Fannie does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Fannie reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.