Does the God-Emperor of humanity have a name, or is he recalled only by his title? For example from what I have seen, he is called The Emperor, The Emperor of Humanity or The God-Emperor of Humanity. Never a name or something related
He had a thousand names over thousand years - he has been known as Gilgamesh, Hercules and Saint George, but his first, original name is a secret.
In the "Pariah" novel its suggested (although it might be incorrectly) that his name is an Ennuncia - word of power, speaking which can change the reality itself, although even trying to read and remember it is very difficult (and potentially deadly) to the reader.
In the the novel "Scars," its implied that Magnus knows it, or at least has a very decent guess.
So answering your question - he does, but only he remembers it.
The emperor also is keeping his name a secret. From the Horus Heresy novel Prospero Burns:
‘When you know someone’s name, you have power over them. Why do you suppose no one knows the Emperor by anything other than his rank?’
So, it was forgotten a long time ago and Big E makes sure it stays that way.
In the Siege of Terra book Saturnine by Dan Abnett, John Grammaticus has a conversation with the Perpetual Erda, in which the following is said:
"Does He have a name, otherwise?"
"Many. He has had many names over the millenia, none of them His own. I have no idea if He has ever had a true name. I knew Him as Neoth."
"Neoth? His name is Neoth? Thats crap. And a huge disappointment."
"No, thats just how I knew Him. It was what He called Himself when I met Him."
Given Erda is the
Mother of the Primarchs (insomuch as she is their female genetic donor and helped the Emperor create them)
and knew Him at the "time of the First Cities", before the Emperor had started his shepherding of humanity (make of that what you will, but its extremely early in the 40K timeline, well before the Horus Heresy era) I think she would be best placed of them all to know the Emperors true name, if he had one.