Index's full name is "Index Librorum Prohibitorum", based on a real book with the same name. It's a list of publications deemed heretical, anti-clerical or lascivious, and banned by the Catholic Church. Source
Does this book also exist in Index's world, and was she named that by the Church deliberately? Or did the author just get the name because it sounds cool?
It's based of the real life list, "Index Librorum Prohibitorum," which in English is literally a "list of prohibited books." Index herself is, in other words, a literal embodiment of these books prohibited by the Roman Catholic Church by Pope Paul IV.
The list was created to protect the faith and morals of the faithful by preventing people from reading of immoral books or works there church thought was heretical. Some of the works even included scientific works by leading astronomers, like Johannes Kepler, whose ideas were controversial at the time. The list basically contained the rules set by the Roman Catholic Church relating to the reading, selling, and censorship of books.
Taken from Wikipedia
Her mind has been implanted with the 103,000 magical texts of the Index-Librorum-Prohibitorum as she possesses Photographic memory, which makes magicians wonder if she really is human because just one grimoire is poisonous to the mind, and one is more than enough to kill a person without the proper preparative.
