One way is to look at your hobbies or interests. Say you love reading, then a name like 'The Bookish Private Page' could work. Another idea is to think about the emotions you want to convey. If you want it to seem warm and cozy, perhaps 'My Cozy Confidential Corner'. Also, you can take inspiration from your favorite quotes or song lyrics and modify them to fit as a name for your snap private story. For instance, if there's a line in a song that says 'My little hidden world', you could use 'My Little Hidden Snap World'.
Think about your personality. For example, if you're a bit of a dreamer, you could name it 'My Dreamy Diaries'.
You can also base it on the kind of content you'll be sharing. If it's mostly about your travels, 'Private Travel Tales' would be a good name. Consider using words that evoke a sense of secrecy like 'Hidden', 'Secret', or 'Exclusive' in the name.