I think he'd follow the same pattern of having a mild-mannered reporter as a secret ID, but there'd be less emphasis on Clark Kent and more on Superman. Look at Captain American and Thor. They practically have no secret ID's even though they're well established. That's how Supes would be treated.
However, I think he'd have a better rogues gallery, and a more defined role possibly. He might be treated more as a cosmic superhero a la Quasar or Captain Mar-vell than as an American icon.
