Perhaps 'Hidden Journeys'. This name implies that the stories are like personal journeys that are hidden from others. It gives an air of mystery and privacy, just as a private story should be.
Well, 'Intimate Chronicles' is a good name. It conveys that the stories are about personal and perhaps emotional things that are private to you. 'Solitary Sagas' is also great as it can suggest that these are stories that are yours alone, not to be shared with just anyone. And 'Privy Passages' which has an old - fashioned charm and really emphasizes the privacy of the stories.
You could name it 'My Secret Garden', which gives a sense of a personal and private space full of unique things. Another option is 'Personal Reflections', as it implies that the story is about your own thoughts and experiences. Or 'Hidden Gems', suggesting that there are precious and private things within the story.
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.