There is absolutely no freaking way that Gordon wouldn't know that it's not the Batman he's used to, and I don't think it would take him all that long to figure out that it's Nightwing who has become Batman.
Of course he knows. And I like to think he knows who it is under the cowl as well. He knows Bruce was Batman, he knows Dick was Nightwing and now Batman... he just pretends not to know it - or doesn't try and get concrete proof at least - because otherwise he might have to arrest them. It's just plausible deniability.