Since I tend to take things so literally and to the point, I would interpret this phrase "be the real you" to mean the me that is raw and unadulterated. Yet there must be more than one layer of "the real you." There is the person that I show to strangers, the one that I show to acquaintances, and then those that I show to close friends and family. Some, or all of you, get glimpses of this person. But unless I know you well, you probably haven't seen all of me, or at least the part that makes me uniquely me. I think this is true about most of the world. As humans it is our nature to just share enough to interact and have friendships but rarely do we really dig deep to get to know someone.
However, when I thought more about this phrase I wondered if in the effort to be our real selves we might actually create this ideal or desirous person that we say we're like. We try so hard to attain this ideal "real personhood" that we fail to actually be who we are, faults and all. In essence, we end up covering who we are with who we want to be and mask who we really are.
So I guess my encouragement is to be who you are with flaws, mistakes, and everything else. Trying to be someone you're not is a waste of your life. You'll totally miss out on the joy of being who you were created to be. This doesn't mean that you totally ignore trying to become a better person but just don't do it from wrong proves because you feel like you won't be accepted otherwise. There are people who love you. Even if you don't feel it, God loves you so much to that he sent his son to die for you. If nothing else take comfort in that.
Finley as a last word of encourGement I leave you with a po from Erin Handon my all time favorite poet. This comes from her book The Poetic Underground. 
