And let's not even talk about Vader NOT knowing Leia was his daughter when he was interrogating her with a MIND PROBE! Sure, she could have hidden her knowledge of the Death Star tape whereabouts, but everything else would have been an open book, especially with his super sith force powers.

Yeah, but Leia does not know Vader is her father, so I assume Vader can't feel that she's his daughter. Even on the Death Star trench he just sens that the Force is strong with Luke, but that's all.

I suppose that, after the battle of Yavin, the name of Luke Skywalker became quite famous in the galaxie for being one of the leaders of the rebellion. So that's why the Emperor and Vader knows his name in ESB.