You cannot be private on the internet, once you have an e mail address it is there for all the world to see, you have to come off all social media to be private, never buy anything on line, do nothing, have no computers, smart phones, nothing.
Only YOU can see that. Other people see your user name on comments. Go back to that question and answer and your comment and you should see your user name. It freaked me out too at first, but then I realized what was happening.
Then you have nothing to be concerned about. I left my email address for someone in the comments section and once I knew that she had it I deleted it as well. You used to be able to contact people through a third party system but like other things they did away with that a while ago.