Ok, my theory for the book – so far.
I don’t think the book changes. The stories are all from a different time/space, somewhere in the past, and seem to written by someone who have seen them happen or heard of them – I like the Blue Fairy/MS theory, specially after ep.20.
So, unless the writers (of the show) are going to a very intricate path, I don’t think current events change to pages.
And about the names, well, most of the fairy tale book are written in this particular style, and most often not all of the names – if not none – were told. Like this story, from the Grimm’s book –
“There was once a widow who had two daughters—one of whom was pretty and industrious, whilst the other was ugly and idle. But she was much fonder of the ugly and idle one, because she was her own daughter; and the other, who was a step-daughter, was obliged to do all the work, and be the Cinderella of the house. Every day the poor girl had to sit by a well, in the highway, and spin and spin till her fingers bled…”
And the story goes on and on and the girl is always “the girl” The poor girl”, etc. So it’s possible that the book is not written in the same way as we hear the flashbacks from FTL, but more, flourished. Also, I think there’s more presented to the spectators as there’s presented to Henry, at least details.