When Rey meets Han on the Millennium Falcon, she knows plenty about his smuggling days. She seems in awe of him when he reveals himself, like she has grown up hearing about him. Do we know who told her about him?
Rey read about the Falcon (and Han's exploits) in salvaged Empire/Rebellion data-files that she'd salvaged.
Rey’s head was spinning. She had read data file after data file about that famous ship and its role in the war against the Empire. Thirty years before, it had fired the shot that took out the Death Star and ended the war. And that was just one of its many heroic adventures.
Finn looked a little starstruck. “Han Solo? The Rebellion general?” “No, the smuggler!” Rey said, recalling the Millennium Falcon’s most infamous claim to fame. “This is the ship that made the Kessel Run in fourteen parsecs!”
As you see in the seventh movie, most everyone on Jakku has to scavenge to get parts from the fallen Star Destroyers, so like the answer above says, she could have found some left over data files and read about Han Solo's past. Another possible answer is that Han Solo is known pretty much everywhere because he made the Kessel Run in less than 12 parsecs, or that he smuggled a lot of stuff on many different planets and got in to a lot of debt with many people.