Some names might be 'Faithful Reflections'. This name implies that the private story is about the deep and faithful thoughts and experiences within the Christian faith. 'Divine Inspirations' could also work, as it shows that the story is inspired by God. Or 'The Holy Happenings' which simply tells that it's about things related to the Christian holy or sacred.
Other possible names are 'Personal Parable', 'Secret Script', 'Intrinsic Story'. 'Personal Parable' can be used if the private story has some sort of moral or lesson within it that is personal to the teller. 'Secret Script' makes it seem like there is a written or unwritten script of a story that is secret. 'Intrinsic Story' gives the feeling that the story is an essential and private part of someone's life or experience.
Some other names could be 'Exclusive Episodes', 'Private Pages', or 'Confidential Chronicles'. These names give a sense of something that is only for a select few or for your own personal records. For example, 'Confidential Chronicles' implies that it's a collection of stories that are private and perhaps a bit like a journal that you don't want everyone to see.
Well, there are many names that could be suitable. For example, 'Natalie', which means 'born on Christmas' and has a warm and friendly connotation. 'Zoe' means 'life' and can bring a positive energy to the private story. Also, 'Sienna' is a name that has become more popular in recent years and has a stylish and unique touch.