Fable stories have a rich tradition in English literature, and they are often referred to by the term “fable” itself. However, if you’re looking for a more specific name for a fable story in English, you might consider the following:
Aesop’s Fable
Traditional Fable
Moral Tale
Animal Fable
Fable Story
These names are commonly used to refer to short, didactic stories that convey a moral lesson through the use of animals or mythical creatures as characters.