((OK, omit that delivery part))
Ethan looked out the window and sighed. They hadn't believed his story. Two cops in an unmarked car were parked, he noticed the car when he first arrived at the room, and there was only one reason why two guys will stay at a parked car in front of a hotel. He supposed the had grabbed the story blindly, as a kind of '**** you' to the police for ruining his plan to get out of the hospital with Carth and that other guy. He was going to have to find them soon. He first dialed Carth's place. He asked his mom to tell Carth to meet him where they were supposed to have lunch. He also wouldn't tell her what was up, but she recognized him from when he used to live in the city and agreed to give Carth the message. He paced around for awhile, and decided to play with the cops a little
He dialed room service and asked them to bring sandwhiches out to the cops' car. He then went down to the lobby, bribed a hotel worker to let him out through the side door, walked down a back alley, to the other side of the block and hailed a taxi while the police would be busy trying to convince the room service guy to leave them alone.
Vader's wife was very pregnant when she died 19 years ago. All of a sudden a 19 year old who is very strong in the force and has a distinct resembalance to him in his younger days rolls in from Vader's home planet with his old Master Obi-Wan (Who was the ONLY other person preset at the time his wife died. And to boot, the kid's last name is Skywalker.
So in answer to your question, he knew Luke was his son because his name is Darth Vader, and not Darth Retard.
-Forum post on why Vader knew Luke was his son.