A Snapchat private story name refers to the name or title given to a private story on the Snapchat platform. Private stories are a feature on Snapchat that allows users to create a story and share it only with a select group of friends. The private story name is the name you choose to give to your story, which can be seen by the members of that private story. It can be any creative and descriptive name that reflects the content or theme of your private story.