It's worth noting that the Force appears to allow some measure of telepathy/empathy: Vader doesn't realize that he even has a daughter until he feels Luke worrying about it on the Death Star.
So...
Knowing that Bail Organa is one of the few people they can trust (i.e., why they're giving him Leia in the first place), and that he's remaining a Senator, it's entirely possible that Obi-Wan and Yoda don't tell him deliberately, because if the worry that Vader will discover Leia is his daughter is in the back of his mind whenever he sees him, Vader could realize it too.
If Bail figures that Vader is just some powerful dark-sider in armor, there's no reason for him to be specifically concerned, even privately.
Also, I know the EU doesn't mean beans with you guys
, but for what it's worth LFL has written somewhere that in the OT era Vader is setup as a loyal Jedi hero who helped the Empire against the traitorous Jedi, but he's presented only as Darth Vader; the name Skywalker never comes up publicly.
So...
Knowing that Bail Organa is one of the few people they can trust (i.e., why they're giving him Leia in the first place), and that he's remaining a Senator, it's entirely possible that Obi-Wan and Yoda don't tell him deliberately, because if the worry that Vader will discover Leia is his daughter is in the back of his mind whenever he sees him, Vader could realize it too.
If Bail figures that Vader is just some powerful dark-sider in armor, there's no reason for him to be specifically concerned, even privately.
Also, I know the EU doesn't mean beans with you guys
, but for what it's worth LFL has written somewhere that in the OT era Vader is setup as a loyal Jedi hero who helped the Empire against the traitorous Jedi, but he's presented only as Darth Vader; the name Skywalker never comes up publicly.


