I mean Luke knows his own last name is Skywalker. He doesn't hide it.

BUT.....does that mean people think Anakin = Vader. No. I always thought the general populace was probably told a lie by the emperor and the media(like our own) swallowed it as gospel and ran with it.

Something like: Headline: "Tragic death to Clone Wars Hero" etc, etc

I also think the timeline is a bit screwed up. The clone wars should happen sooner in the timeline of the PT and then be finished by ep. 3 to have some space.

By the time of ANH the jedi are almost talked about in mythical ways.