Spiderman has Peter Parker. Wonder Woman has Diana Prince. Groot has...well, he's just Groot.
The point we're trying to make is that all most superheroes have secret identities, and The Incredibles are no exception. The only difference is that in The Incredibles, superheroes have been banned by the government, leaving our titular heroes with nothing but their boring secret identities to keep them warm at night. Far from being an easy transition, this seismic shift shatters our heroes' sense of self, leaving them unsure of who they are now that the capes and cowls are catching only dust bunnies in the corner closet.
Questions About Identity
Why are superpowers so tied to identity for Bob and Dash?
Does Helen struggle with her own sense of identity? Why or why not?
How does Bob's sense of identity change over the course of the movie?
How does the idea of a "secret identity" for a superhero relate to the film's themes?
Chew on This
Because Bob spent so much of his life as Mr. Incredible, his superpowers are unavoidably associated with his sense of identity.
Bob's growth over the course of the film is the merging of his two primary identities: Bob the father and Mr. Incredible the hero.