^ Well, I mean, if I were Obi Wan or Yoda at the end of Revenge of the Sith thinking about what to do going forward, I would have A LOT of problems with hiding Luke on Tatooine. Kenobi’s plan is actually even worse than simply hiding Luke on Tatooine. He’s not only hiding Luke on Tatooine, but hiding him with a person that has a direct family connection to Anakin. Kenobi didn’t just throw Luke at some random orphanage in Mos Espa. He placed him with Anakin’s step-brother Owen. I mean… talk about a witness protection disaster. There are so many risks involved here. It’s possible somebody from Owen’s or Anakin’s past might one day blab about this boy appearing out of nowhere, or any number of things or past associates of Anakin or Owen could accidentally leak information that could ultimately alert Vader to investigate. Even if there’s only like a 0.001% chance of it happening, why take the risk? Tatooine is one of the few places in the Galaxy with people who used to know Anakin.
I mean ultimately all of this is a big writing kludge, because A New Hope was never written with the idea that Luke is supposed to be hiding. It makes no sense his last name is still Skywalker. People try to justify this with various excuses, like “maybe Skywalker is a common name!” or whatever. Again, I don’t care, because why risk it? If your last name is Smith and you go into witness protection, they will still change your name. They certainly changed Leia’s last name.
As things stand, the explanations you provide are probably the best we can do given the material we must work with, but it’s still kind of a kludge and an unfortunate side effect of the retcon that Vader is Luke’s father. Don’t get me wrong, I absolutely love the idea that Vader is Luke’s father. It’s one of the best retcons in movie history. But it does come with certain unfortunate side effects like making Luke’s living situation and the fact his name is still “Skywalker” seem absurd in retrospect.
You know, I think it’s not that difficult to explain why they decided to keep Luke’s original last name. If you think about it, Shmi’s last name was also Skywalker, which means there’s probably a whole side of the Skywalker family that we know nothing about. After all, for Shmi to be called Skywalker, her father had to have that last name too, and so did her grandfather, her great-grandfather, and so on. So, it’s entirely possible that there could be other members of the Skywalker family on Tatooine or perhaps other planets, and they probably decided that Luke could keep his last name for this reason. Just because someone is called Skywalker doesn’t mean they’re directly related to Anakin and Padmé, so Obi-Wan and Yoda probably thought Luke might have been confused with another distant member of the Skywalker family who had nothing to do with Anakin. And it’s not like Vader was actively going around the galaxy looking for his distant cousins or other family members, he wanted to forget everything about his past and his family.