Presumably the M name was inspired by C, the nickname given to the mi6 chief in real life.
The C comes from that being what the first chief of mi6 used to sign, his surname was Smith-Cumming. Interestingly, he also famously said, after it was discovered that human semen works well as invisible ink, that "Every man his own stylo" - rather appropriate for a man named Cumming.
"Eve Fleming's nickname from her son Ian was M and Ian may have used his relationship with her as model for M, fictional head of Head of the Secret Intelligence Service and James Bond's boss."
That doesn't make it true, but it does seem to have some evidence.
The C comes from that being what the first chief of mi6 used to sign, his surname was Smith-Cumming. Interestingly, he also famously said, after it was discovered that human semen works well as invisible ink, that "Every man his own stylo" - rather appropriate for a man named Cumming.
edit: wiki says that staff under him used that phrase, I'm not 100% sure he coined it or not. https://en.wikipedia.org/wiki/Mansfield_Smith-Cumming