What is M's real name?

As noted in Wikipedia, (the Judi Dench) M's real name is very likely Olivia Mansfield. The source for this entry is this article on comingsoon.net which reveals:

There was also something else that cropped up while we were looking through the archive, something that may be of even more interest to Bond fans. As we looked at the porcelain bulldog M bequeaths Bond, the archive assistant read the inscription on the box it is presented to him in - "Olivia Mansfield bequeaths James Bond." We've searched around, and as far as we can see this is the first and only time anyone's ever revealed M's 'real name.' It may not have been spoken, but if you were watching on a big enough screen it could have been visible, so we'd argue it's now canon.

This site also provides a screenshot:

Besides the use of a single letter to represent the head of MI6, this might be a further homage to its very first director who was—as noted by Steve Melnikoff—named Mansfield Smith-Cumming (or C).

I think the house-keeper called her Emma because Em is short for Emma so he just makes the logical assumption that this is her nickname.

I also think that M means something like Master as Q is referred to in Skyfall as Quartermaster.

I strongly doubt that M has any direct link to her actual name as that would suggest that hire people based on their own name as all people holding that position in all the bond films have been known as M.

To answer your specific questions -

What is M's (Jude Dench's M) real name? - nobody knows.

Is that her true identity? - nobody knows.

If yes, how does he come to know of it?? - Living in a world where people usually don't have codenames he would have assumed that Bond said Em, not M, and it was short for Emma. Whether her name is actually Emma and it was a coincidence? - nobody knows.

M's name is not revealed in the movies.

However, if the use of "M" as a code name was based on it being the first letter of the surname of the first person to occupy that role, then this reflects real life, as the first head of the real MI6, Captain Sir George Mansfield Smith-Cumming, signed his documents as "C", as have all his successors.

So, this suggests 4 possibilities:

• M is the first head of the fictional MI6.
• She's not the first M, but both her surname, and the first M's surname, begin with "M".
• The head of the fictional MI6 is always referred to by the first letter of their surname, and it's just coincidence that, in this case, they both begin with "M".
• None the above, and it is really is a randomly assigned initial, or is short for "Master" or something similar.

I vaguely recall from a documentary that I saw about Flemming that it started out as an abbreviation. The person in charge, when he read documents, would sign them 'M' as it was his initial.

After a while it grew into being his name because it was easier to say than 'Section Commander ...'. When he stepped down/was pushed aside the next person continued to use M as their signature as everyone was calling him M anyway. Hence is became a kind of code name.

It clearly has to do with her actual name as she wouldn't have hit so snippy with him when he said that a few films ago. But I do not think her name is Emma. That's just an old geezers assumption and would he totally coincidental.

This is the M from Ian Flemings' short stories. Not the movies. Keep that in mind.

The only fact I would add to the answers above is that in the books (Moonraker and The Man with the Golden Gun) one of the M characters is named as Sir Miles Messervy. M was his initial.

My guess is that the character M was carried over into the films, Judi Dench was cast and the initial continued. A name through evolution rather than because every person who held the position of 'M' had a name beginning with M! The line is most likely a throwback to this relationship (after all Casino Royal was Bond's first double-O assignment).

I don't believe we can know for sure.

"M" could be the British short form for Mom. Mom is the British word of respect for a woman.

James Bond refers to her using both M and Mom in the film.

British military may refer to a female officer as Mom instead of Sir.

It's disrespectful to refer to a man as Mom, which is why Bond might have referred to her replacement at the end of the film as M. He was the guy who got shot in the arm (sorry, can't remember his name).

I remember when Bond calls him M he says it almost sarcastically.