Alice: Where is this love? I can't see it, I can't touch it. I can't feel it. I can hear it. I can hear some words, but I can't do anything with your easy words.
Dan: At six, we stand round the computer and look at the next day's page, make final changes, add a few euphemisms for our own amusement.
Alice: Such as?
Dan: "He was a convivial fellow" - meaning he was an alcoholic. "He valued his privacy" - gay. "He enjoyed his privacy" - raging queen.
Alice: What would my euphemism be?
Dan: She was... disarming.
Alice: That's not a euphemism.
Dan: Yes, it is.
Larry: Is he a good fuck?
Anna: Don't do this.
Larry: Just answer the question! Is he good?
Anna: Yes.
Larry: Better than me?
Anna: Different.
Larry: Better?
Anna: Gentler.
Larry: What does that mean?
Anna: You know what it means.
Larry: Tell me.
Anna: No.
Larry: I treat you like a whore?
Anna: Sometimes.
Larry: Why would that be?
Larry: Dan, I lied to you. I did fuck Alice. Sorry for telling you. I'm just not big enough to forgive you, Buster.
Larry: You don't know the first thing about love, because you don't understand compromise.
Larry: What would happen if I touched you now?
Alice: I would call security.
Larry: And what would they do?
Alice: They would ask you to leave and ask you not to come back.
Larry: And if I refused to leave?
Alice: They would remove you. Those are security cameras in the ceiling.
Larry: I think it's best I don't attempt to touch you. I'd like to touch you. Later.
Alice: Why isn't love enough?
Larry: A good fight is never clean.
Answer: It appears so. Nothing else suggested he knew where she worked. More that he was just going to different clubs and drinking and came across the club Alice was working at.
Lummie ★
I think he knew exactly where to find her. He's a doctor and often doctors are known to have that "God" complex. I think he wanted to gain control of his relationship with Anna. To win Anna back he had to manipulate all the players including Alice/ Jane. He probably researched her and found her. That's why he knew Alice/Jane was not her real name. He was low key stalking all of them, to get Anna back.
But Jane actually was Alice's legal name. This is shown at the end of the movie, on her ID. Larry did not believe her when she told him.
At the strip club, Larry does *not* know that her name is legally Jane. He thinks her name is Alice. She is using a stage name at the club, and he wants to hear her say that her name is Alice. He refuses to accept "Jane" as the answer. He is waiting to hear "Alice."