In the Post-Crisis comics at least, there are multiple statements indicating that it is not widely known that Superman has a secret identity.
BATMAN: By going maskless as Superman, you divert most people from thinking you might spend part of your time as someone else. After all, it's not likely you'd wear a mask in civilian life.

Adventures of Superman Vol. 1 #440 (May, 1988)
SUPERBOY: See, the Bat-guys--they wear masks and slink around in the dark, but with us S-guys--we're all about truth! I mean, we keep other people's secrets, but when it comes to us--everything's on the table! No disguises, no secret I.D.'s...
STEEL: I don't know, kid--sometimes I wish I still had a secret identity.
SUPERGIRL: And... and how can we really know that, say, Superman--or any of us--doesn't have one?
SUPERBOY: Excuse me--Superman? If the Big Righteous "S" had a secret life, we'd know 'cause he woulda told us!

Team Superman Secret Files and Origins Vol. 1 #1 (May, 1998)
SUPERMAN: My name... I'm really nervous... my name is Clark Kent. I'm a reporter for the Daily Planet. And this is really not easy for me... so feel free to say something.
GREEN LANTERN: He doesn't... wear a mask. I never even... thought he had a... day job.

JLA Vol. 1 #50 (February, 2001)