In the Doctor Who episode "Journey to the Centre of the TARDIS" (S07E10) we saw Clara wandering off corridors of the TARDIS and finding this particular book.
She starts to read it, during which she says:
So that's Who..
We know for sure that she saw The Doctor's name, because of the dialogue at the end of the episode, just before the time is rewritten:
Clara: The library. I saw it. You were mentioned in a book.
The Doctor: I'm mentioned in a lot of books.
Clara: You call yourself Doctor. Why do you do that? You have a name. I've seen it in one corner of that tiny...
The Doctor: [shushing her] If I rewrite today, you won't remember. You won't go looking for my name.
Who wrote the book and why? Can we know the answer for sure?