But that's not a category mistake.

Really?

What is Lois actually looking for? When we say she's looking for Superman, we mean she's got a search target in her mind, a conceptual representation of Superman, and she's looking for something that matches that target closely enough to satisfy her. (Or, well, we ought to mean that. What we actually mean, I'm less sure of.)

If I introduce the typographical convention <x> to designate a conceptual representation of an object X and the convention m(x) to designate an object that matches a concept x, then Lois is looking for m(<Superman>).

Superman is Clark Kent, but <Superman> is decidedly not <Clark Kent>. To expect that because Superman is Clark Kent that Lois is looking for m(<Clark Kent>) sure sounds like a category mistake to me.

One nice thing about this is that if you know the secret, then in your mind <Superman> starts to resemble <Clark Kent> very closely... they aren't identical, but any m(<Superman>) is almost undoubtedly also a m(<Clark Kent>) and vice versa. Which is exactly what we would expect -- the more I believe Clark Kent and Superman are one and the same, the more likely it is that if I'm looking for one I'll terminate the search upon finding the other.