You may consider 'Personal Musings'. This name is suitable because a private story often contains your own thoughts and daydreams. It's a space where you can muse over different aspects of your life, your hopes, and your fears without any external interference.
My Inner World
Think about the main theme or emotion of your story. Maybe it's love, adventure, or mystery. Use words related to that to come up with a name.
You could name it 'My Secret Adventure'. It gives a sense of something exciting and personal that you don't want to share widely.
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.
You could name it 'My Secret Chapter'. This gives a sense of it being something personal and exclusive, like a chapter in your life that only you know about.
You could name it 'My Secret Adventure'. It gives a sense of mystery and personal experience.
You might want to draw inspiration from your personal experiences or interests when naming your private story. Maybe there's a place, a hobby, or a special memory that could form the basis of the name. Or, try combining words that have a special meaning to you.
You could name it 'The Secret Adventures'. It gives a sense of mystery and fun, like there are some really cool and exclusive things that happened in that story.