Your identity online is a question of who you want to be.
Do you want to provide a recorded history of your thoughts and life to the world? Or only those finalized, edited, and made perfect to associate with your static identity? The internet provides both unparalleled opportunities to socialize and unprecedented degradation of the ability to be human in a fluid, ever-moving fashion (that is, where history is relegated to the participants' imaginations and not primary sources in digital history books).
Our selves are both formed and built by our interactions with the world — it's why social media can depress us; when we lose ourselves, I'd go as far as to say it's from fabricating and curating a personal image. And these platforms can encourage that.
The physical world affords us plenty of opportunities to build a fake persona, but also natural opportunities to form a self as we'd like. There are quiet places we can go in the real world to not be judged for our thoughts and actions — at the least, within the walls of our own homes. But the design of much social software makes this more difficult to do; raises the stakes on every interaction; makes it harder to act naturally.