Star Wars can be about a lot of things. Actually I see Star Wars as a genre onto itself. It is a western/mythology/knights/war/romance/sci-fi/adventure mixed together in a beautiful way. It's more about the world that was created, Jedi, Sith, The Force, aliens, odd planets etc. But having adventures with in them. The Clone Wars (great series) showed how versatile Star Wars can be in terms of genre. Foloni and his team created many different episodes with completely different styles/themes. From film noir, to dark revenge tales. Star Wars is versatile. It's more about a feel, a genre, a style that is Star Wars. Again many video games and books that are nothing to do with the main story have proven that.
The EU (yes we know it's no longer canon but it's still there in terms of stories told) showed through video games, books, comics, that some of the best ones had nothing to do with the characters we know. KOTOR showed you can go beyond names, and still retain the Star Wars world and spirit. The Dark Forces Series did that as well. Even a lot of episodes of TCW did. Rebels will have almost nothing to do with them. Even the people at Disney realize that Star Wars is much bigger of a universe then just them. If they limit themselves to that then it will get stale quickly Because Disney will want to show how vast this universe is. We have had 6 films, they will be making many many more. So we only have those 6, but that does not mean the future has to always been just one family. But with the main episodes it's clear they are following to a point the blood line.
The name Skywalker is a great name, I love it, my dogs middle name is that. But it's not the core of Star Wars. It is the genre, the story of good vs evil, a genre onto itself. Shows like Rebels and TCW show you can go beyond what the films have done, and still have as wonderful Star Wars stories out there.
To get involved with characters, just having a name is not enough, or really the main thing. It's all about just good writing, good story telling. Star Wars is a vast scope, and it's massive scope has allowed it to be in various mediums, some with great quality, video games, books, comics TV shows etc. Star Wars can go to many different areas and stories, and still be Star Wars. Otherwise it would have fallen into oblivion a long time ago.