The received wisdom around DC fandom, I understand, is very much that while Bruce Wayne is really Batman, Superman is really Clark Kent, which I like.

It generally is, although you'll get a few outliers. Also skewing the whole issue... I'm now realizing... Bruce Wayne is SUCH a creation to throw suspicion away from him being Batman... and SO MANY (all excluding Alfred, I'd say) of his personal relationships are made when he's Batman.