This Los Angeles Times story about California’s redesigned voter registration form also discusses the American Independent Party. The article reveal that some California county election officials want the legislature to pass a law making it illegal for any party to have the word “Independent” in its name.
Tennessee has a law making it illegal for any party to have the word “independent” in its name, but that law was held unconstitutional by a U.S. District Court a few years ago as a violation of free speech. Later the Sixth Circuit reversed that on the grounds that none of the plaintiff political parties had standing to challenge that law, because neither of them had “independent” in their names. The plaintiff political parties in that case were the Green Party and the Constitution Party.