General:
* Narrator
* Chronicler
* Bard
* Troubadour
* Minstrel
* Griot
* Fabulist
* Mythmaker
* Tale-spinner
* Wordsmith
Focusing on the art of storytelling:
* Weaver of tales
* Spinster of yarns
* Conteur
* Oral historian
* Storyweaver
Focusing on the audience:
* Entertainer
* Enchanter
* Captivator
* Charmer
* Magus (for someone with particularly powerful storytelling)
Focusing on the content:
* Historian
* Biographer
* Novelist
* Poet
* Playwright
* Screenwriter
Informal:
* Yarn-spinner
* Storyteller
* Tale-teller
The best synonym will depend on the specific context and the desired level of formality.