R2D2 and C3PO are the models of the droids. Much like AMD 3500+ and Nvidia 6800GT...just because you only own one of each, lose it for some time and find the same type doesn't mean it is yours.
I am sure they each have serial numbers, but I doubt obi-wan memorized those.
If someone related to vader was on tatooine people would talk about that, it would be interesting to them. Word of that would spread fast and reach the ears of eager sith and eventually vader himself. Obi-Wan was in charge of watching over luke so I am willing to bet they were pretty far from mos eisley(nearest largest city, I believe). He did this to keep him away from people that would be looking for him, and to keep people from spreading word or suspicion of him.