Possible Plot hole, or my confusion about a line Vader says

Vader didnt know who Luke was because he didnt even know who he was anymore

I don't understand why this is considered to be a plot hole. We don't know exactly when Vader hears the name "Luke Skywalker" (sometime between Ep 4 and Ep 5), but we can assume Vader immediately realizes Luke is his son.

Ep 5 starts with Vader, "obsessed with finding young Skywalker." Again, obsessed because it's his son and Vader wants to use Luke to overthrow the Emperor. Indeed, Vader reveals this exact plan to Luke at the end of Ep 5.

The Imperial troops are obsessed with finding Skywalker because (rumor has it) Luke delivered the shot heard 'round the galaxy, vaporizing their comrades on the Death Star. So, motivating the troops with "I'm sure Skywalker is with them" seems natural. Luke is the Osama Bin-Laden of the day. Poster child of the rebel scum. So, it also makes sense that Vader wouldn't casually mention, "yeah, that's my kid" to any of his Imperial lackeys.

Later in Ep 5, the Emperor tells Vader that Luke is their "new enemy" and Vader's like, "damn, the Emperor's on to me, I better play along or I'll get the business end of the finger lightning again."

The Emperor even uses the phase "the son of Skywalker" while talking to Vader so again, no surprise to either of them that Luke is Vader's son.

The Emperor has a plan to replace the aging Vader with young Luke. Indeed the Emperor reveals this plan to Luke at the end of Ep. 6. So when Vader says to the Emperor, that Luke would be a powerful ally if turned to the dark side, the Emperor is like, "damn, Vader's on to me, I better play along or respirator boy won't help me find Luke." So the Emperor is like, "yeah yeah, capture Luke alive, that's a good plan that you just came up with. Let's do that."

So everybody knows everything except for Luke who is a pawn in this power struggle between Vader and Palpatine.

That's a good question. I'm not certain of the answer but I think Vader is not Anakin Skywalker, but even so he knows that Luke is either his son or long-lost brother.

Darth Vader is like Anakin Skywalker reborn. He probably still had memories of Anakin Skywalker. So he knows all about Anakin. Anakin had no meaning to him and therefore Luke doesn't either, Anakin is his past life which he doesn't care about, so he doesn't care about Luke. Maybe he knew the Luke is his son, but if he doesn't care about Anakin, why is Luke any different?

i think he knew luke was his son. and if not then at what point does he learn that he is the father of luke? they share a last name and he later tells him that he is lukes father...either that or skywalker is just a very popular last name in a galaxy far far away :)