Such a person is typically called a short story writer.
The common name for someone who writes short stories is a 'short story author'. They focus on crafting concise and engaging narratives within a limited word count.
A person who writes short stories is typically called a short story writer.
A person who writes stories is typically called an 'author' or a 'writer'.
Well, the usual name for someone who writes stories is an 'author'. Authors come up with all kinds of tales and share them with the world through their writing.
A person who writes short stories is usually called a short story writer.
A person who writes stories is commonly called a 'writer' or an 'author'.
A person who writes fiction is usually called a fiction writer.
A person who writes stories is commonly called an author or a writer.
A person who writes stories is called a storyteller or an author.
You could call them a story scribe. This term emphasizes their responsibility of putting your story into words. Generally, 'author' is the most common and widely understood term though.
Such a person is often referred to as a memoirist. They focus on recounting their own or someone else's life experiences in detail.