I really can't say I see this as a plot hole. If you need an indication in the film that Vader knows who Skywalker is when Empire begins, it's right there in the opening crawl. "Vader, obsessed with finding young Skywalker". It's not like it's a huge leap of logic to think that Imperial Intelligence, between the Battle of Yavin and the battle of Hoth, discovered the name of the Rebellion's big hero. the name alone is enough to spark Vader's interest, the fact that he has felt the force in him, before he knew the name, is enough to make sure that when he does get the name, he can put it all together. "Hmmm, kid whose last name is skywalker and is strong in the force... Possibly was in the company of Obi-Wan Kenobi and came from tatooine. Naaaah, probbly just a coincidence."

It seems perfectly logical to me that bewteen Star Wars and Empire, Vader has been informed of Luke's name, why we need something explicitly stating when and where that occurs, I don't know. We never see the characters sleep or use the washroom in the trilogy, but I think we can assume they do. It just doesn't require a scene to show it.