It takes a second for the words to process and then he's sighing loudly and biting the inside of his cheek. "And I came here going through some portal but I forgot about it. Great. And if I'm in your past and you know about where the Cave is, you probably know my civilian identity which means you currently have the high-ground right have." Not to mention he knows what's happening and Dick doesn't.
Dick makes a move toward the elevators. He wants to see everything in here and if he can avoid having to ask Nightwing's help, he will.
So far, he's been useful but nothing indicates if he's lying or not (Dick knows the basics about what to look out for but all he can tell is that Nightwing looks sincere).
"I'm guessing asking for your name is pushing it, huh?" He's not really expecting an answer and so he goes on, "Are you going up? I want to see the rest of it."