Vader didn't know that Luke was his son until the Emperor told him...
Doesn't matter when he knew that.
how did Vader know that Luke was Obi-Wan's apprentice? Was it an
assumption?
Lessee.
He knows that the droid containing the DS plans was sold to the Lars farm.
He knows that a chick named Skywalker once lived there.
He knows that same droid was on a beatup YT-1300 freighter that blasted out
of Mos Eisley.
He knows that that same beatup YT-1300 freighter landed on the DS with
Obi-Wan aboard.
He knows that a rebel strong with the Force was later flying an X-Wing down
the DS trench and that he wasn't there to drop off pizza coupons.
He also knows that a droid matching the description of the droid carrying
the DS plans (and that looks suspicously similar to his old astromech R2
unit from the Clone War days) was riding on that X-Wing.
And at the start of ESB, he knows there's a rebel named Skywalker and he's
all hot to find him.
Put all these facts together and I think even Anakin could figure out that
Skywalker was the Force-using rebel and that it was Obi-Wan who trained him.