The entirety of Star Wars is replete with plot holes if we dwell too much on it, so we try not to. Some of those are simply due to the fact that as Lucas expanded the Star Wars mythology his course through the twisting maze ran squarely into a wall, and instead of reversing the path, he applied some White Out to the obstruction and hoped you didn't notice. It's not meant to be an insult. Lucas had no idea his passion project would turn into a franchise. He ran into problems that have plagued comic book writers for decades. It's difficult to tell a cohesive narrative over the course of a half century.
And that is the real answer to the titular question of this article. The real world answer is that when A New Hope was written, Luke and Leia weren't envisioned as twins, Anakin Skywalker and Darth Vader were definitely not the same person, and Vader was not Luke's father. The second James Earl Jones uttered the, "No, I AM your father," line, a pinhole sized plot hole was introduced. When Leia and Luke became twins, it was the size of a hole punch. When the PT established that the choice hiding spot for Luke was literally the planet where Anakin Skywalker grew up and first met Obi-Wan Kenobi, William "The Refrigerator" Perry burst through that hole during pre-game introductions. This all started during a conversation with Mrs. Other Guy:
Me
There's a lot of speculation over who the "Skywalker" in The Rise of Skywalker is.
The Missus:
Unfortunately because Carrie Fisher passed away, it's probably not Princess Leia.
Me
Well Princess Leia's not really a "Skywalker". She's an Organa from when they put her in hiding and she was adopted.
The Missus:
So why did Luke keep the Skywalker name, then?
Me
Uh...uh... ... ...I don't know.
I can usually spit ball an excuse for a Star Wars plot hole pretty easily. It might not hold up under cross examination, but at least it will buy me time. I was stumped with this one. I've since come up with some weak ones, but has there ever been a explanation for why Luke's ancestry was only partially obscured, while Leia's was placed on double secret probation? The concept that Owen and Beru would have had a biological son would have been the most effective way to hide Anakin's progeny.
Barring a better explanation, I'm going to say that Owen never liked the boy and refused to give him his name.
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See that Krayt Dragon swallowing the sandrawler over there? I'll allow you to be Luke Lars if we eat Krayt steak for dinner tonight. I'm going inside to watch Archie Bunker.