The Supreme Court has protected the right under the First Amendment to anonymous speech, except when it hasn't (as when it has upheld campaign contribution disclsoure laws, where the interest in anonymity was overriden by other important social goals). In Does 'The Freedom of the Press' Include a Right to Anonymity? The Original Understanding Robert Natelson
examines
legal and historical evidence to determine whether, as some have
argued, the original legal force of the First Amendment’s "freedom of
the press" included a per se right to anonymous authorship. The Article
concludes that, except in cases in which the press had been abused, it
did. Thus, from an originalist point of view, Supreme Court cases such
as Buckley v. Valeo and Citizens United v. Federal Election Commission,
which upheld statutes requiring disclosure of donors to political
advertising, were erroneously decided.