Importance of Identity?

I have just begun reading the book Every Day by David Levithan, and, of course, within the opening chapter I am already reminded of Invisible Man.

The basic idea of the Every Day's story is that the narrator (an unnamed storyteller) is stuck with the reality of 'becoming' a new person each day. In this 'becoming', the narrator in essence inhabits the body of someone who was already living, taking over their entire life as that thinking, breathing pre-existing person for a day. In the opening paragraphs of the book, the narrator describes his perpetual experience: "Every day I am someone else. I am myself--I know I am myself--but I am also someone else." Literally, the narrator wakes up each day to have yet another different form to house his some unseen yet sentient essence. However, the narrator has over time become somewhat content with this phenomenon, saying "I don't know how this works. Or why. I stopped trying to figure it out a long time ago. I'm never going to figure it out, any more than a normal person will figure out his or her own existence. After a while, you have to be at peace with the fact that you simply are."

This story reminded me of Invisible Man due to its heavy focus on the importance of identity. And after reading the first part of Every Day, I question, is identity actually important? In reality, we have many labels to describe us and give our existences shape. But are they all necessary? Can one live without an identity, or with a fluid one? I think so. After all, the narrator of Invisible Man finds comfort in being socially "invisible".