I have always thought that "M" was an arbitrary company assigned code name, a thought shared by Bond in Casino Royale (remember the scene where he broke into M's apartment?). But there have been hints to that it has something to do with her real name.
MAJOR SPOILER ALERT for those who are yet to see SKYFALL
The house-keeper of Bond's ancestral house, back in Scotland refers to M as Emma.
Is that her true identity? If yes, how does he come to know of it??