The divide between "real name" and "pseudonym" is very fuzzy as soon as you step outside the "engineer box" and look at real world data. Many people in this world go by names that you would never expect to see on their driver license or passport, both of which seem to be things Facebook asks users provide to "prove" their "real names".
And lets not even get started on the fact that facebook is in fact part of real life. If people call you a certain name on facebook, they are calling you that in real life. Different names for different social situation is far from unheard of. Which is "real"?
My ex goes under 3 first names. Her legal name is an African name that few people in the UK can pronounce. Two largely non-overlapping sets of her friends call her by two different English names that are "close" to her legal name. Only some people in her family usually call her by her legal name.
Which is her "real" name? Most people use one of the English names. She responds the same to all three.
If she had to use her legal name everywhere, most of her friends would be unable to find her, as few of them even know her legal name. What makes her legal name more or less "real" than the others (which are used more, by more people)? Why?
Your legal name is Jonathon but friends know you as Johnny.
Should you be reported to facebook HQ for not using your legal name?
What if your nickname distorts its origins further, such as "J", which easily turns into "Jay". Have we know left the realm of Real Names?
What if you prefer to go by a middle name? Or an ethnic nickname which doesn't have an obvious relationship to the original (i.e. Alexei -> Alyosha). What about the common practice of adopting a "Western" name for people who native names translate poorly into English?
Is a facebook employee qualified to judge whether you're using your real name?
Did you mean legal name? And if so does that exclude legal aliases?
What about Madonna, is that her 'real' name?