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 stories is typically called an 'author' or a 'writer'.
A person who writes short stories is typically called a short story writer.
Such a person is typically called a short story writer.
A person who writes stories is commonly called a 'writer' or an 'author'.
A person who writes short stories is usually called a short story writer.
A person who writes fiction is usually called a fiction writer.
A person who writes stories is called a storyteller or an author.
A person who writes stories is commonly called an author or a writer.
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.
They are usually very imaginative. They can create entire worlds in their minds and then put them down on paper. For example, Tolkien created Middle - earth for his 'Lord of the Rings' series.