My only issue with it is that she figured out who he was before
he was even Superman. In effect, she never figures out that Superman is Clark Kent. She instead discovers that Clark Kent is just some dude who has superpowers. I'd have much rather have had Superman be known to the world first, and then have her figure out who he was from there (with no need for her having ever met Clark Kent, let alone be in any kind of relationship with him, romantic or professional, first).
In the movie, he never really adopts a secret identity. He adopts a hero identity.