How does Luke Skywalker not already know that Vader's his father at the end of Empire Strikes Back?

Film  Never mind the prequels (although they certainly help) but this video which turns the destruction of the Death Star into a parody of 9/11 conspiracy videos has inadvertently ruined the Star Wars trilogy just a little bit more for me because at a certain point I asked this question which has never occurred into me in the many decades since their release.

How does Luke Skywalker not already know that Vader's his father at the end of Empire Strikes Back?

As we know this was a big surprise for audiences on the release of the film, barely spoiled thanks to the internet not having been invented, schtum journalists who agreed that giving away the ending of the film was morally wrong (unlike now) and fans who wanted to save the delight for their fellow humans.

Anakin's name wasn't revealed until Jedi.  But as this video suggests by spelling the whole thing out, George Lucas's slight of hand leads us to ignore the following logic:

That none of the imperials have questioned who Darth Vader is.  Where he comes from.  He's a disciple of the Emperor  fine, but how did he gain his position in the imperial fleet and how did he manage this without someone asking for more about his identity in the whole vastness of the fleet.  At some point, something has to be leaky enough that someone, somewhere will know that he was originally Anakin Skywalker, Jedi Knight.

Given that, how is it then possible that none of the rebels would have this information either?    If intelligence is amazing enough that some Botham's can steal the death star plans, admittedly at the risk of their own lives, surely the rebels would have some kind of intelligence base, part of who's mission is deep background on who they're fighting.

Apart from anything else, there's a galaxy full of oppressed people who lived under the Old Republic and through the clone wars and know who Anakin was.  You could have an discussion about whether it was simply assumed he died along with the other Jedi (and I'm aware I'm straying into prequel information but nevertheless, the Jedi are a lost force in the sacred trilogy) but neverthless it's entirely improbable that the rebels wouldn't know that Darth Vader was originally Anakin Skywalker.

If you do invoke the prequels, there's a range of people who might put two and two together, the whole administrative staff on Coruscant for a start.

Which brings us back to Luke.  Luke's walking around with his surname.  Given everything above, how unlikely is it that someone wouldn't walk up to him at some point and say, you know that Darth Vader.  You know his original surname was Skywalker?  Did he come from the same planet as you?

Unless Skywalker is the intergalactic equivalent of Smith, that coincidence would seem remarkable, even if it wasn't generally know that Anakin had children.

Because the other option is:

Darth Vader just sort of exists.  He's there when the imperial senate takes control of the galaxy installed by the Emperor.  No one knows who he is or where he comes from and frankly they're not likely to mess with them because he'll kill them.

The rebels, some of whom are old enough to have fought in the Clone Wars, haven't the foggiest either.  He's just some guy, a Sith lord.

Luke Skywalker spends his life on a farm being lied to by his doomed Auntie and Uncle and Old Ben Kenobi and he's entirely oblivious of his real origins taking everything which is told to him at face value until Darth Vader reveals his identity to him and us.  He's as surprised as we are.

How does Luke Skywalker not already know that Vader's his father at the end of Empire Strikes Back?

It really is all just a fairy tale isn't it?