If I create a written book, I'm aware that it can be copied. However, could other players on a multiplayer server copy my book, and, if so, who will be listed as the author?
The author of the book is set when you "sign" it, after that point it cannot be changed and creating a copy will give a book with identical author and contents to the original.
So the only way someone could change the author, would be to re-write the entire thing themselves or edit the files if they're the owner of the server. (This may also be possible with mods, but I don't know of any)