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.
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 call it 'My Secret Chronicles'. It gives a sense of it being a personal and private account of events in your life. Another option is 'Hidden Tales', which implies that the stories within are not meant for public consumption. And 'Personal Reveries' also works well as it suggests private thoughts and experiences.