No need to add disclaimers to ideas here, Darth. It's actually similar to an idea I had at one time to have Skywalker be a name given to Anakin when he performed a "miracle" of piloting for a primitive species. Your idea is better though.
I got the feeling from watching Return of the Jedi that it was the Anakin part of Anakin Skywalker's name that evoked Vader's ire. "I know that you were once Anakin Skywalker, my father." Luke added emphasis to Anakin, not to Skywalker. So I think that it may be better to have Lars as the name that Owen and Beru took when they went into hiding, Owen's real name being Skywalker. Of course, the name Lars is never mentioned in the OT proper, so it can be assumed that their names are Skywalker, but it makes sense that they don't use those names in public. It wouldn't make sense for Luke to keep the name Skywalker if it was given to him by Obi-wan, for Owen would never tell him that it was his name, disliking Anakin as he did.
Nobody seems to recognize the name Skywalker in the OT. Even Leia, who knows the history of Obi-wan Kenobi, doesn't seem to understand the significance of Luke's name. Lando is totally ignorant of it as well, and he may have been around 20 years old at the time of Anakin's fall (though I think that the time of his fall should be pushed back at least ten to fifteen years in this rewrite). This seems to suggest that Skywalker was not a well-known name in the galaxy, or at least people didn't attach significance to it. I'm guessing that Anakin Skywalker is the name that his parents gave him, because I doubt that Anakin would be a name chosen by him as a Jedi title. Remember also that according to ANH, Anakin was not a Jedi when he left Obi-wan, so Obi-wan could not have given him any Jedi name.
I like the idea that Yoda gave Ben his Jedi name of Obi-wan. This makes sense in the context of the story. However, if we're examining all of the evidence, it suggests that Anakin Skywalker, the name given by his parents, was changed by Anakin himself to Darth Vader, going beyond the single first name change and creating a new identity, twisting the ways of the Jedi. Darth is not a title, it is his literal first name. "You can't win Darth."