I've been a fan of the privacy, osint, security scene for some time. I regularly see people getting confused about being private and being anonymous. These are two different animals.
To be anonymous you have nothing linking back to you. It's not your name, your real email, picture, anything really. It's all fake or not even mentioned. You are more of a ghost. This is very useful if you are a criminal, investigating criminals, or living somewhere it wasn't safe for you to be yourself in a public sphere. Speaking out against your government for example.
Privacy doesn't have to mean people can't identify you, it's more about them knowing you. I don't mind if you know my name, but do I want you to get access to my phone number or address? I may not want the world to know my kids or other family members details either. So I don't share it. But my social profile still has a real picture of me and my real name. This is being private.
Privacy is the common solution. Most people you encounter on places like twitter may want to be recognized. They are possibly building a brand, seeking recognition, or networking for a job. To do this doesn't mean you have to tell the world everything about you.
I would say anonymity actually hurts a little in online communities. Imagine you have been on twitter for a couple of years. You've helped some opensource projects or non profits as your anonymous self throughout the years. Suddenly you need to find some work. Will you be able to reference that past work? Even if your not afraid to out yourself, could people trust it was you?
So you pick what works for you. Again, for most people to stay safe online you need to exercise privacy. Anonymity is for more extreme situations in my perspective.
Be sure to let me know what you think..you can send me a tweet.