Not sure how Anakin’s background would be handled. Perhaps he was ashamed to have been brought up on a farm and even claimed to be an orphan, while changing his surname from Lars to Skywalker? Also I have no idea if why and how Obi-Wan changes his name to Ben. That could very well happen off-screen, between the trilogies, I think.

About the names: Simply, Beru Skywalker married Owen Lars. Or is that TOO simple? ( I would give Owen and Beru a bigger part at the opening of the saga) For Jedi, it was recognized as a ancient religious order, so how about Obi-wan being his chosen name when becomes a knight (Like Roman Catholic nuns). When the Jedi fall, he goes back to his given name, Ben. It makes Leia’s message in IV more interesting: She calls him “General Kenobi” and “Obiwan- Kenobi” separately. Almost like “General” and “Obi-wan” shouldn’t be said in the same sentence. Also, you can start the story with Kane Skywalker (from early Lucas drafts) who becomes Anakin when he becomes a Jedi.

Also, the Republic has a professional army (pre-stormtroopers of sorts). The purpose of the Republic is very much aligned with the principles of the Jedi, as it is a loose federation of planetary systems that work together towards common goals. Only after the war erupts does the Republic begin its transformation into a different body, with a tighter grip. Only at this point the idea of separatism slowly begins to sound the same as treason.

What if different worlds originally have their own militaries, but as the Clone Wars progress, paranoia and distrust between Republic worlds leads to a centralization of the armed forces into the Republic Army… then the Empire? If the Clones are the Antagonists, the enemy could be right next to you and you wouldn’t know it. This could explain why Alderaan would have no weapons of their own in IV.