A apocraphal story might also be known as a dubious story. The term 'apocraphal' implies that the story is of doubtful authenticity. It may have arisen from misinformation, hearsay, or the creative imagination of individuals. In this sense, 'dubious story' captures the essence of an apocraphal story as something that cannot be easily trusted or verified.
Another name for an apocraphal story could be a unauthenticated story. Apocraphal stories are often not part of the official or recognized canon. They might be legends or rumors that have been passed around without solid evidence to support their truthfulness. So, unauthenticated story is a fitting alternative name.
A apocraphal story can be named as an unsubstantiated story. Such stories don't have enough proof or evidence to back them up, just like when we say a claim is unsubstantiated. They float around without the necessary factual basis, much like rumors that may or may not have any truth in them.
A yarn can also be another name for a story. This term is often used in a more informal or folksy way. People might say 'spin a yarn' which means to tell a story, usually one that is interesting or perhaps a little exaggerated.
A chronicle. A chronicle is more like a record of events in the order in which they occurred. However, it can also be seen as a type of story, especially when it is told in a more engaging and narrative way, like historical chronicles that describe the lives of people and the events of a particular time period.
A short story can also be called a novelette or a short narrative.