I would think Leia coming from Alderaan legitimately through Padme having been Queen of the place in her youth might have been too much of a clue even for the likes of Darth Vader. Even if one nods at Luke being from Tatooine, like Anakin was, it tracks in that Vader doesn't want to go there as their are too many painful memories there. If the original concept of Padme having survived childbirth and gone into hiding with Leia had happened, having them hide out on Alderaan, of Padme had been Queen of Alderaan in TPM would have been way too much. And as teenaged Princess /Senator Leia becomes a public figure, even someone like Vader's gonna notice. But with Padme being from Naboo, and buried there, it throws the track off for the likes of Vader.
He has no clue he had a daughter until his last day. He hadn't even considered it. But if this young firebrand Senator had been from the same planet as Padme, Vader would take notice of her and mentally be reminded of Padme...and that's dangerous. Because there would be that chance of finding two and three and making five with the realization that this teenager is about the age his child would have been, and that she's from the same world as his wife, and she's in the same occupation as his late wife.....and she has some surprisingly familiar droids.......