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 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.
Forbidden Journeys. It's a great name as it creates an air of something that is not meant to be widely known or accessible. It gives the idea that the private story contains adventures or experiences that are special and not to be shared openly.
The Hidden Tales. You can use this name as it gives a sense of mystery and exclusivity which is perfect for a private story. It makes the reader or viewer feel like they are about to discover something that is not for everyone.
Personal Chronicles. This name gives the idea that it's about your own personal stories that are only for you or a select few. It has a bit of a classic and timeless feel to it.