There are many things you should be able to do publicly without repercussion from your employer. However, your example is berating them, and I'm taking that literally: "to criticize in an angry manner".
If I read this correctly, then you believe your employer should be able to fire you if you angrily criticize them in public under your name. I agree in principle, that could damage their trust in your ability to do your job. Depending on specifics, that damage could be enough to justify firing you.
I don't understand why doing so anonymously should change the potential damage to their trust in you, if they later learn you said what you did.