Not exactly, but close. Obi didn't know if Leia would be a Jedi or not. She never showed any powers even in the retconned Kenobi series that I'm aware of. The only example of Leia using the Force was Ep 8 where she flew back to the shuttle and then they mentioned Luke trained her after the end of the war for a while. Now maybe Yoda could sense that Leia was Force sensitive, not just Luke and Obi Wan couldn't. That's the best argument you can make for the stupid retconning of giving Force powers to her after that Obi/Yoda exchange.
Technically Yoda's robes were pretty similar to Obi's also, even if his looked like a potato sack because he was an actual puppet
Now the first part, why would they go to Tattooine and not change Luke's name ? Their excuse, I mean, "explanation", is that Anakin fucking hated Tattooine. He bitched about the sand in Phantom Menace. It's where he was a slave, where his mom died, where he slaughtered the sand people. Anakin, before or after Vader, never had any intention of stepping foot on that planet again. He also thought his kids died and had no reason to ever look for kids that didn't exist. The real question is, despite the Emperor telling him that they were all dead, why couldn't he ever sense their presence? He might of talked himself out of it. I can't remember if it's in the theater release of Revenge of the Sith or if it's an alternate ending or if it was in Tales of the Jedi, but there's a funeral of Padme where she's carried down a street. They intentionally made her look pregnant so everyone thought the babies did also. So there was a BIG effort to retcon why Vader never looked for his kids.