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.
How about 'The Mysterious Meanderings'? It gives a sense of intrigue to your private story. Another option could be 'The Hidden Hilarity'. It implies that there are funny things in the story that are only for those who are privy to it.
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.
Look at the mood or theme of your private story. If it's a story about a wild night out that you want to keep private, you could call it 'The Rambunctious Rendezvous Reminder'. Consider using puns as well. For example, if your private story is about trying to find something and it's private, you could name it 'The Quest for Quietude'.
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.