Fanon would say that Doctor is an alias he gave himself. After all, what kind of parents name their kid Doctor, or even Master, for that reason. The Doctor has always been vague on this, refusing to elaborate on this title he's given himself. The writers know they can't just reveal his real name, it would ruin the mystique and mystery.
When the show started out, this was fine. He was a mystery man with a mystery past. However when other Time Lords are introduced, they also refer to him as the Doctor. You'd think they would know his original name. I compare it to Kryptonians calling Superman "Kal-El" or Themyscirians calling Wonder Woman "Diana."
My thoughts on this are based on a little examined aspect of Gallifreyan culture..
Not all Gaillfreyans are TimeLords. The TimeLords are the elite nobleborn. While not exactly stated, it would be reasonable to assume that lower class Gallifreyans can't regenerate. It is perhaps worth noting that when the Doctor talked about being the last of his kind, he only referred to TimeLords and not Gallifreyans, would he have cared if other people from his planet were still around?
In The Caretaker, Danny Pink referred to the Doctor as aristocracy and an officer and the Doctor was enraged in the way only a penetrating truth can evoke. He is an aristocrat. Sure he mingles among all different races and classes, but he's still used to being treated as a TimeLord.
So my theory is that in this noble class, when a young TimeTot reaches the age of maturity, they pick a name that is used thereafter. Much like in our world, Lhamo Thondup is referred to as The Dalia Lama, Andrew Albert Christian Edward is called The Duke of York, etc. It is a cultural thing for TimeLords to use this instead of their birth name. It's not that they don't know his name, but they respect his position in their society. And this applies no matter what a TimeLord has done, such as The Master or The Rani. When the Doctor returns to Gallifrey in Hell Bent he bides his time in a barn and is visited by a kindly older woman. She doesn't refer to him by any name, but I got the feeling she knew the Doctor when he was younger (perhaps all Gallifreyans have long lifespans compared to humans) and may have known his birth name and been the kind of person who could get away with using it. Like you could imagine Pope Francis having a grade school teacher or babysitter who could get away with calling him "little Jorge."
This would also explain why the Doctor and Master, who are said to have been childhood friends, never refer to each other by other names. Why condone his delusions of being a Master, unless it was part of the conventions you grew up with. Even the detractors of people like Popes still acknowledge the title.
We can thus assume this applies to other TimeLords like Rassilon, Borusa and The Rani. Maybe even Romanadvoratrelundar, or she just wasn't old enough to go through the ceremony when she met The Doctor.