Most likely she would have been with the SVR (the successor organization concerned with foreign intelligence) or the GRU (it's Ministry of Defense equivalent). But you're right that most Americans (and others) probably wouldn't recognize what those are, while "KGB" is pretty universally understood. (Just like most people would probably recognize the defunct "INS", but might not know what "ICE" is.) (The "F" organization you're probably thinking of is FSB, which is the successor organization to the KGB concerned with internal security and counter intelligence.)