Well, 'Intimate Chronicles' is a great name. It makes it clear that it's about personal and close - to - the - heart stories. 'Soul's Whispers' can also be a nice name. It gives the feeling that the stories are like the quiet whispers of your soul. And 'Private Musings' is suitable too, indicating that it's for your own musings and reflections.
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.
For a cool name for your private story, consider 'Exclusive Exposures'. This name gives the feeling that the content inside is something special and only available to a certain group or just you. 'Solitary Sagas' is another option. 'Solitary' indicates that it's something private and alone, and 'Sagas' makes it seem like there are epic or interesting stories within. Also, 'Secret Scrolls' can be a good name. It has an old - world charm and the idea of a scroll being something that holds precious and private information.
Another option is 'The Whimsical Wonders'. This name implies that your private story is full of wonderful and unexpected things in a really light - hearted way. It makes it seem like a magical collection of experiences.
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.