From word of mouth
One cannot "just start" a myth. Myths are the result of oral traditions that go back thousands of years before they are ever written down; passed down from word of mouth from generation to generation; sometimes before a culture developed writing.
Oral history is history that was not written down as it happened but after it had been passed down by word of mouth. Great grandparents told their children who told their children who told you. It was also stories that were handed down from generation to generation in cultures so that it would be remembered. Eventually it would be written, but when it was finally written there were no living wittnesses.
The Vedic information was a 'jealously guarded secret' of an influential group of individuals called Brahmanas. The information was memorised and passed on to the next generation by word of mouth.
There is a Latin word 'thema' meaning a subject or a thesis. The same word in Greek is a proposition or a subject as in 'something set down'. This word was adopted into the French language in the 13th Century and changed to 'temse. (the 's' may well have been silent.) The word then passed into general European usage, adopting the local language variations
I think it's called oral tradition.
A story with fanciful elements, which may or may not be historically verifiable, that has been passed down by word of mouth for many generations.
They are called myths
An oral story is typically referred to as a "folktale" or "oral tradition." These stories are passed down through generations by word of mouth rather than being recorded in writing.
A story or legend passed down from generation to generation is called oral history, oral tradition, or folklore.
Unfortunately the author of Beowulf is unknown, because it was passed down orally (by word of mouth, through story telling) generation after generation. Sorry!
Voodoo does not have a holy book. Rather, it is passed down by word of mouth.
No Aboriginal music was passed down through word to mouth. Meaning they never wrote it down.
Many have been passed down by word of mouth throughout centeries.
Legend
There is no known course of mythology; most authors are anonymous. But, most are passed down by word of mouth, generation to generation.
Anything passed down by word of mouth is an oral tradition. Anything taught by the church would be a ecclesiastical tradition. So it looks like you're looking for an oral ecclesiastical tradition.