If what you're looking for is a decentralized pseudonymous system. Then this is absolutely possible with today's cryptography.
It's called public-private keys. You create a private key that you can use to "sign" your messages. And people can verify that is was you that wrote the message by using the public key.
No one can pretend to be you because only you have access to your private key and the public key can't be used to find out what the private key is.
It's still anonymous because you don't have to say who you are when you create the private key.
It's not perfect because the same person can create as many different keys as they want. So you can't really "ban" someone. They'll just create a new key and pretend to be someone new.