If you read the Crawl, "A group of freedom fighters led my Luke Skywalker" refering that he is leading Rogue Squadron. It does say they established a new base on Hoth, meaning they found a planet suitable enough to hide from the Empire.
And changing "young Skywalker" to "Luke" doesn't need to change. We are refering to Darth Vader speaking and that is what he called him majority of the movie