Some really cute names could be 'Twinkle - Toes Tales'. The 'twinkle - toes' is a cute and girly concept, and when combined with 'tales' it makes for a great name for a girl - only private story. Another option is 'Sunshine Secrets', which has a positive and cute vibe. And 'Flower - Friend Fables' is also a lovely name. Flowers are often associated with girls, and 'fables' gives the sense of a story, while 'friend' makes it seem more exclusive among girls.
Well, you could go for something like 'Ella's Intimate Tales', which gives a sense of personal stories. Or perhaps 'Sophia's Secluded Stories' that implies a private collection of experiences. Another option might be 'Olivia's Confidential Chronicles' as it sounds like a private account of a girl named Olivia.
Some nice names could be Lily, which represents purity and beauty. Another option is Sophia, meaning wisdom. Also, Ava, which has a modern and sweet feel.
You can choose based on the personality you want to give the girl in the story. For example, if she's strong - go for something like Brianna. If she's shy, maybe a name like Violet would work.