The Crane here is different from the one back home. He's basically from an alternate reality.

But see, that's kind of my point. I told you who I am and what I do because I trust you, and I assume that's why Tim told Sylar. We don't just hand this stuff out to people. Knowing this information can get people killed back where we're from, or at least put them in serious danger, and I just don't get why he'd be that fast to tell someone about it. I mean, obviously the Barge is a really different environment? But if he wanted to be Batman on the Barge, why bother introducing himself as Bruce Wayne to people? And why pick now to reveal himself to everyone?

And frankly, a "oh, just so you know, I'm beating up Crane and telling him I'm Batman, which then totally blows your cover, and probably Tim's too" would have been nice.