Canonical sources for time around The Last Jedi and after it are sparse so far, so I don't think we can provide definitive answer yet. Maybe upcoming novelization will change that.
However, junior novel The Legends of Luke Skywalker does provide some insight into minds of galaxy youth and status of Luke Skywalker at around this time. Here is what we know:
- Luke spent years after Battle of Endor travelling galaxy far and wide. He met a lot of people and a lot of people witnessed first-hand some of extraordinary things he is capable of. He was subject of numerous stories shared during long space travels, in cantinas of dubious reputation and probably in many other places.
- Some of stories about Luke were greatly exaggerated or not true at all. One Imperial Battle of Jakku veteran believed that Luke single-handedly brought down two star destroyers - while it isn't yet established in canon if he was even present during Battle of Jakku.
- Children working in Canto Blight stables had access to crews of numerous starships from around the galaxy. They definitely heard some of the stories circulating around.
Some blanks are still left to be filled by your imagination, but we can at least try to answer some of original questions:
But there could be thousands of competing stories vying for people's attention.
At that point of history, Luke popularity was already established. That was not some random story competing for attention with other random stories - that was new story about very popular superhero. It was willingly shared thanks to the same mechanisms that make new Star Wars trailers go viral.
Why is the true story more successful?
We happen to know that this particular story is somewhat true, but in-universe it's status is probably similar to other stories about Luke. Children find it fascinating because it's super-awesome. Adults dismiss it as myth or think that there is some element of truth somewhere deep down below layers of fantasy.