I agree. And yes, I think it's highly possible that Threepio was made out of parts from many different Droids. Still, it's the processor/brain/personality thing inside his head that counts. I think that as long as he has no memory of any possible adventures he may have had before Anakin built him then we shouldn't consider him the same Droid. Kind of like reincarnation, which some people believe happens to you after you die. However, personally I believe that if you have no memory of your past life, you have a different name, you are brought up in a different enviroment and by different guardians then you aren't even the same person you once was. Your personality, looks and opinion on certain things will be completely different, making you a completely different person.
I hadn't thought of that DD. It's a good point that you have raised. Where did the program come from? Was it residual froma previous incarnation or did Anakin create it.
I know this has been said many times before, but I thought I'd add it to the mix.
When Threepio says "Thank the Maker", he's basically thanking Anakin or worse of all Darth Vader.