Well, you could also go for 'Christmas Chronicles Unveiled', 'A Private Christmas Memory', or 'Secret Santa Stories'. These names give a sense of something personal and related to Christmas at the same time.
Think about your own personal experiences during Christmas. If you had a special moment by the fireplace, you could name it 'By the Fireplace: A Private Christmas'. Another way is to use alliteration, like 'Private Presents at Christmas'. This makes the name catchy and unique.
Some other names could be 'Wreath Whispers (Private)', which gives an air of secrecy and Christmas charm. 'Gingerbread Gossips (Private)' is also fun, as gingerbread is a popular Christmas treat and 'gossips' implies personal stories. And 'Carol's Closet (Private)', which makes you think of a private place where you store your Christmas stories, like a closet, and carols are an important part of Christmas.
Friendship's Hidden Hideout. This name shows that the private story is a hidden place where the secrets and special moments of your friendship are stored, away from the rest of the world.