In recent years, he simply doesn't have to. Superman is careful (a) to act differently than Clark, and (b) not let anyone know that he even has a secret identity.
As far as most people are concerned -- and there have been stories where ordinary folks discuss this -- Superman spends his downtime at his Fortress of Solitude, or the Watchtower, or someplace like that. Clark Kent is just a guy who resembles him.
And if that's not good enough, remember that time Superman rescued Clark from beneath a collapsed building? All the news programs showed video of Superman shaking hands with Clark. (And by "Clark" I mean the shape-shifter Matrix who was happy to help out.)
Okay, that's a digression. But the point is, facial recognition isn't enough to prove that two people are the same person, especially if no one is inclined to believe it.