Obviously from the movies we know a lot about the Death Star.
But when the Falcon approaches it no one is aware that it's a space station. So on one hand, I'd think the Empire kept it rather quiet.
On the flip side, they blew up an entire planet so I assume the secret is kinda out.
Clearly the Alliance would know about a giant space station that is threatening their very existence.
But what about people not involved in the Galactic Civil War? Would someone on Tatooine know about the Death Star? Do they know that the Empire destroyed Alderaan (Wookiepedia seems to say yes). And then what do people know about its destruction? Do they know it was destroyed? Do they know it was a single ship or do they think it was a massive Rebel armada? (Emkay's comments in X-Wing Alliance notwithstanding.)
Just want to make sure I reference the Death Star correctly in my campaign.