[Roger Thornhill's matchbook carries the initials RoT.]
Eve Kendall: What does the O stand for?
Roger Thornhill: Oh, nothing.
Roger Thornhill: The moment I meet an attractive woman, I have to start pretending I have no desire to make love to her.
Eve Kendall: What makes you think you have to conceal it?
Roger Thornhill: She might find the idea objectionable.
Eve Kendall: Then again, she might not.
Roger Thornhill: I don't like the way Teddy Roosevelt is looking at me.
Answer: Not really. You could (and at some hotels are still able to) keep your room number private or you could not - i.e. you could ask the hotel staff to keep your number secret from strangers, or you could ask them to tell anyone who might ask. Not having seen this movie, I don't know how likely it would be in the situations you speak of that the hotel guest would choose the latter option- it might be a mistake.
Blibbetyblip