I didn't catch your name
I didn't hear your name. Typically prompts the listener to repeat their name. A: "Sorry, I didn't catch your name." B: "I'm Joe. Nice to meet you."
I didn't catch the name, and I didn't catch your name.
I don't remember your name.; I didn't hear your name when we were introduced. Bill: How do you like this weather? Bob: It's not too good. By the way, I didn't catch your name. I'm Bob Wilson. Bill: I'm Bill Franklin. Bob: Nice to meet you, Bill. Bob: Sorry, I didn't catch the name. Bill: It's Bill, Bill Franklin. And you? Bob: I'm Bob Wilson.