Did most people throughout the galaxy know of Luke Skywalker's role in destroying the first Death Star?
I would suspect the rebellion would keep his role a secret since they would not want the empire to target him.
Did most people throughout the galaxy know of Luke Skywalker's role in destroying the first Death Star?
I would suspect the rebellion would keep his role a secret since they would not want the empire to target him.
Luke’s role in destroying the Death Star was quickly publicized, despite Alliance efforts to keep it secret:
The Rebel Alliance romanticization of the everybeing fighter pilot truly began after the Battle of Yavin. For his safety, Rebel messagesmiths avoided publicizing Luke Skywalker’s name, but the tale of a young Rebel pilot with minimal combat experience who destroyed the Empire’s ultimate weapon was too powerful to keep secret for long.
Star Wars Propaganda: A History of Persuasive Art in the Galaxy
Indeed, this was shortly after the Battle of Yavin. By the time of the New Republic, of course, the story was widely known, with everyone having heard "the big story," which was so widely known that conspiracy theorists concluded that it could not possibly have happened:
“To this day, they’ve never adequately explained what happened to the first Death Star. Yes, we all know the big story, Luke Skywalker single starfighter blah blah blah, but honestly, does that sound credible to you? The Empire had the greatest engineers in the galaxy, and the Death Star was their finest achievement. There’s no way it could’ve been vulnerable to that kind of attack. The Emperor had to have been betrayed by someone on the inside.”
Bloodline
I imagine, as time went on, Luke's exploits would filter out. I mean, they did kinda have this big awards ceremony at the end of Episode IV. There's a LOT of people there who knew what Luke did.

Consider also that Lando thinks he gets pegged to lead the assault force in Episode VI because of "his little maneuver at the Battle of Taanab". Rumors naturally float around about impressive stuff like that. "Farm boy beats battlestation" would be quite the sensational story.
But the greatest evidence? Palpatine knew, and he connected the Skywalker name instantly back to Vader. He then tells him in Empire
Emperor: We have a new enemy, the young Rebel who destroyed the Death Star. I have no doubt this boy is the offspring of Anakin Skywalker.
Darth Vader: How is that possible?
Emperor: Search your feelings, Lord Vader. You will know it to be true. He could destroy us.
Darth Vader: He's just a boy. Obi-Wan can no longer help him.
Emperor: The Force is strong with him. The son of Skywalker must not become a Jedi.
MOST people? I highly doubt it. Even in an advanced technological society like the Star Wars galaxy large parts of the civilisation will be rather provincial and backwards with little or no contact with the outside world/universe.
They'd not be interested in, or receive, much if any news from outside their own city or planet.
And with the Empire in control of the media, spreading news of the rebel victory would not be that easy outside of rebel controled space.
So even if the rebels succeeded in using his exploits as propaganda, it would not have reached a large part of the galactic population, at most a large part of the urban population in the star systems they control directly, and maybe parts that are on the fringes of Imperial control (where Imperial censorship and control over the media would be limited).