Ah. There's a book called The Making of Doctor Who (someone correct me if this is not the right title) that came out in the Seventies where the guys (who were scriptwriters and producers at the time) wrote in a bit where the Doctor's real name was written down as a mathematical formula. And theta and sigma have to be code for something, obviously. I love the good old mythological trope of things being created through speech, the way the Logopolitans keep the universe going by speaking complex mathematical formulae and stuff, so in my fanon (of which there are several;)), I kind of like the idea that Timey names are formulae and speaking them is an act of great power. The new series has emphasised that quite a bit, which I like--River whispering the Doctor's name, the Visionary scribbling the Doctor's and the Master's sigils into her Gallifreyan calligraphy predictions... that whole words of power thing. But I digress.

And yeah, you should definitely explore the classic canon more:). Some Doctors absolutely hate being called Theta Sigma, some quite like it. I think Four hated it and Seven loved it, but I might remember wrong.

Love your idea of Theta giving Koschei a book as a gift and him picking up the name from there. D'awwwwwwww!