GoodMusician said:

I wonder how he learned Luke's Full name... I don't remember it being mentioned in ANH... in fact... save for about 10 seconds of Leia screaming "Luke it's too late!" as he kicked some old man clothes on the floor, he never heard the boys name lol...

Leia: "Aren't you a little short for a stormtrooper?"

Luke: "Huh? Oh the uniform! I'm Luke Skywalker. I'm here to rescue you."

Now that the old Emperor dialogue has been changed, this is the only time you hear his entire name in the whole trilogy.

And I think that he'd be pretty famous after destroying the Death Star. In a cut scene, Red Leader actually says that he knew his father. The name Skywalker is pretty famous from the Clone Wars and after destroying the Death Star, Luke's name as the son of Anakin Skywalker, hero of the Clone Wars, must have resonated throughout the galaxy. It's hard to remember that these characters aren't in a bubble that we the fans of the movies are.