But if Anakin would have gone dark after the birth, then he would have known about both of them and wouldn't have needed to find out that Luke existed and then to find out Leia existed from Luke's thoughts during the duel in the Emperor's throne room.
1. In Hope, Obi-wan gives Luke a Blue Lightsabre. And it's the same hilt as Anakin's in the prequels. He loses it in Empire. And the green one with the new hilt is in Jedi. Later, he get's Anakin's back from the Emperor's storehouse on Wayland and gives it to Leia.
2. It's not uncommon for people to invent memories of things they don't remember but think they should.