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.
In Japanese culture, 'kamishibai' was a form of storytelling that involved using illustrated boards. While it's a form, the act of doing kamishibai can also be thought of as a type of storytelling. Also, in some Middle Eastern cultures, 'meddah' was a storyteller, so'meddah -like storytelling' could be considered as another name. These different names across cultures not only represent the act of storytelling but also the cultural significance and traditions associated with it.
There are a few less common ones. 'Story - crafting' is one. It emphasizes the creative process of making a story, like a craftsman carefully creating a piece. 'Narrative - constructing' is also not as commonly used but it shows the building or putting together of a narrative. And 'Tale - concocting' gives the idea of creating a story in a somewhat imaginative and perhaps less traditional way.
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.