Alright, finally got to see it a second time today and like a lot of people have already said, it's better after a second viewing. Probably due to the fact that I already knew what to expect, I could focus a little bit more on the little details and since I already knew the story, some scenes didn't looked as rushed as the first time I saw it. There are still some things that I feel doesn't make a lot of sense or that I think is stupid (looking at you sith dagger...), but the good is good enough to look pass those nitpicks. There is some nice addition to the lore in there and a lot of scenes that feel like Star wars. I'm a big fan of episode 8, and I don't feel like episode 9 tried to retcon it or anything. I still think it's the weakest episode of the sequel trilogy, but still good nonetheless. I would now rate it 7/10.
Now, regarding the Skywalker name in episode 4. He's definelty named Luke Skywalker and not Luke Lars. If I remember correctly, the only time we hear his full name in the movie is when he rescue Leia and says confidently that he is Luke Skywalker. I don't think he would have said it confidently like this if he spent his life known as Luke Lars. Now I might be wrong, but I think we never hear the name of Anakin Skywalker in the episode 4, and the Emperor only refers to Luke as the son of Skywalker. I believe that the first time we hear the name of Anakin Skywalker is in Episode 6 when Obi-Wan explains his certain point of view.