You could consider names like 'Intimate Chronicles'. It gives the idea of a personal and private collection of events. Another option is 'Solitary Saga', which implies that it's a story that is unique to you and not shared widely. 'Private Pageant' is also a good one as it has a sense of a personal and perhaps even a bit of a dramatic story that is only for you.
'My Secret Chapter', 'Personal Reverie', 'Hidden Tale' are great names for a private story.
Some other names could be 'Confidential Chronicles'. This name emphasizes the secrecy and personal nature of the story. 'Secluded Script' also works well as it gives the feeling of a story that is set apart and private. And 'Personal Portfolio of Memories' is a more detailed name that can imply that the private story is a collection of your memories, both big and small, that you want to keep to yourself.
You could name it 'My Secret Chronicles'. It gives a sense of mystery and makes it clear that it's something personal and only for a select few to see.
The Secluded Travelogues. It emphasizes that these are travel stories that are private and secluded, not for everyone to see. It gives a feeling of exclusivity, as if only a select few are allowed to peek into these travel adventures.
Try 'The Unseen Narrative', 'Secret Scribbles', or 'Private Portfolio'.
How about 'Exclusive Exposures'? It makes it seem like the story reveals things that only a select few can see. Or 'Confidential Chronicles' which emphasizes the secrecy and personal nature of the story.
How about 'My Secret Sanctuary'? It gives the feeling that the story is a safe and private place.
Some other names could be 'Exclusive Episodes', 'Private Pages', or 'Confidential Chronicles'. These names give a sense of something that is only for a select few or for your own personal records. For example, 'Confidential Chronicles' implies that it's a collection of stories that are private and perhaps a bit like a journal that you don't want everyone to see.
Think about the main theme or purpose of the private story. If it's about your travel adventures, 'Our Secret Journeys' would be a good name. It gives a sense of exclusivity and relates to the content.