I haven't tried it, but my guess is that File either cannot be extended, or there may be some other limitations related to this kind of classes. I'd go for composition then, that is I'd create a class extending EventDispatcher and expose the name property through it's getter (which you can make bindable). Or, better yet, I would avoid using bindable whatsoever. It is OK for mock-ups and quick demos, but really, there's 0 benefits when it comes to the production code.
