The name Fanya is a girl's name of Slavic, Russian origin meaning "from France; free man". Fanya and is often added to lists like Russian Baby Girl Names and discussed in our forums with posts like "Hunt for our favourite girl names (Alphabet-wise)".
From the experts:
Fanya might make an exotic and unusual short form for the classic Frances, or could stand as a full name on its own. Definitely classier than Tanya but with the same Eastern European flavor.