Some Time Lords have names -- like Rassilon and Romana. And some have descriptions -- like the Doctor and the Master. And, presumably, the Rani; I don't know what the fuck a Rani is but she's a the.
And then there's Omega. Omega's important and I expect we'll be seeing more of him very soon. But his name is sort of an interesting exception in that it's not a the but it's still more description than name.
Of course, Doctor Who's mythology is patchwork. Time Lord society is built across decades of retcons -- hell, nobody uttered the words "Time Lord" for the first six years of the show, or "Gallifrey" for the next five. Time Lord social customs aren't mysterious and inconsistent by design, they're mysterious and inconsistent because they're making it up as they go along. Present tense; they're still making it up.
So I'm sure there's a reason some Time Lords have names and some have descriptions. Maybe it's out there in the books or audioplays somewhere. Or maybe nobody's come up with one yet and it'll be up to some writer to handwave a reason at some point. Hell, maybe both; books and audioplays aren't canon and the show is free to contradict them.
And of course the names operate on another level besides the in-universe one. I'm sure that, in-universe, the Master didn't choose his name because of a double-meaning implying he's second-best after the Doctor; I'm sure that, in-universe, he chose it solely on its primary definition and not its academic one. But even if Letts and Dicks didn't have that double-meaning in mind when they named him -- and Wikipedia says they did, though there's no citation -- then certainly later writers made the connection.
So while I was looking over that Wikipedia entry, I clicked on over to the page for Terror of the Autons, the Master's first appearance. And it's got this bit about the novelization of the episode:
The Master and Doctor are revealed herein to have names that are mathematical formulae
Again, the books aren't canon -- but if the Doctor's name is a mathematical formula, that could certainly be pertinent to the current storyline, now couldn't it?