Does a superhero need to have a secret identity?

I am having some trouble thinking up a superhero name for a girl with photokinetic powers. Then I wondered if she even needed a secret identity or alias. If being a superhero was all she was, would she need a secret identity? What are the pros and cons of having a secret identity and not having a secret identity? And as readers would you find it more believable if superheroes had secret identities or not?