Well, there are several other names for a story. For instance, 'account' can be used when it's more like a factual or detailed description of events. 'Fiction' is also a term that can be considered as another name for a story, especially when it involves made - up elements. And 'chronicle' is another option, which often implies a story that is told in a chronological order, perhaps recording historical events or personal experiences over time.
Some other names for telling a story include 'chronicle - making'. This is like creating a record or account in the form of a story, often with a sense of historical or sequential order. 'Fable - speaking' can also be a name, especially when the story has a moral or a lesson, like traditional fables. And 'anecdote - sharing' is another, which is more about sharing short, interesting stories from personal experiences or things one has heard.
A short story can be known as a novelette in some cases, though a novelette is often a bit longer than a typical short story. Another name could be a short fictional tale, which emphasizes the fictional nature of the story within a short form.