'Spinning a yarn' is also a way to say telling a story. It has a more informal and perhaps even a bit of a creative or fanciful connotation. Sailors used to spin yarns (tell stories) about their adventures at sea, often with a touch of exaggeration to make the story more exciting.
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.
Weaving a tale. It gives the image of carefully constructing a story, much like weaving a fabric. Each element of the story is like a thread that is carefully put together to create the whole.
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.
For example, if the word is 'narrator'. In 'Pride and Prejudice', the narrator is an omniscient third - person who tells us about the lives of Elizabeth and Mr. Darcy. Another word could be 'protagonist'. In 'The Catcher in the Rye', Holden Caulfield is the protagonist and also the teller as he shares his experiences in his own voice. If we consider 'witness', in a crime - based story, a witness to a murder might be the one who tells the story to the police and then to the readers or viewers.