I tried to register a new Twitter account. The registration form said, that my full name will appear on my public profile. Is there a privacy setting for at least limit the people available to see my full name?
The only reason Twitter asks you to enter your real name is so that people you know can recognize you. But, you could also tell the people you want to follow you what your username is so they can find you.
Screenshot of name field in profile settings:
On a side note: if your account is set to be private, your friends/future followers will have to request permission to see your tweets anyway. :-P