Other possible names are 'Personal Parable', 'Secret Script', 'Intrinsic Story'. 'Personal Parable' can be used if the private story has some sort of moral or lesson within it that is personal to the teller. 'Secret Script' makes it seem like there is a written or unwritten script of a story that is secret. 'Intrinsic Story' gives the feeling that the story is an essential and private part of someone's life or experience.
Another option could be 'Intimate Narratives'. This name implies that the stories are something private and close to you, and it has a bit of a mysterious and alluring feel to it.
For a travel journal private story, 'My Solo Travel Escapades' could be a great name. It clearly indicates that it's about your personal travel experiences.
Well, how about 'My Exclusive Escapade' or 'The Privy Plot'? These names can make your private story seem more interesting and special. They give the idea that it's something that's only for a particular group or just for you. Like 'The Privy Plot', it makes it sound like there's a secret plan or story that only you are privy to.
Names like 'My Private Panorama', 'Hidden Histories', 'Confined Chronicles' would work well. 'My Private Panorama' gives the feeling of a complete view of something that is only yours. 'Hidden Histories' implies stories from the past that are not known to many. 'Confined Chronicles' suggests that these are stories that are restricted to a certain group or just to you.
Some names might be 'The Unshared Narrative', 'Private Pages', or 'Secret Scribbles'. These names give the idea of something that is only for you or a select few to know about. For example, 'The Unshared Narrative' emphasizes that this is a story that is not meant to be spread widely, but rather kept within a particular group or just to oneself.