Some good names might be 'Secretive Scribbles', 'Hidden Histories', or 'Privy Personal Stories'. These names give the sense that the story is meant to be very private and only for a select few, if anyone at all. The words 'secretive', 'hidden', and 'privy' all convey the idea of privacy.
Well, consider names such as 'Veiled Vignettes'. 'Veiled' gives the impression of something being covered or hidden, which is perfect for a super private story. Another option could be 'Cloaked Chronicles'. 'Cloaked' is like being wrapped up and concealed, much like the nature of a private story. And 'Whispered Tales' also works well. It gives the feeling that these are stories that are only told in hushed, private whispers.