The California legislature seems likely to pass SB 696, which makes it illegal for party to have “Independent” or “Independence” in its name. In the history of government-printed ballots, 47 states have at one time had a party on the ballot that used one of those words.
In 1908, William Randolph Hearst supported a party called the Independence Party, which ran Congressman Thomas Hisgen for president. It was on the ballot in almost all states.
In 1967-68, George Wallace formed a new party in most states, and in many states it was called the American Independent Party.
There have been ballot-qualified parties named Independence Party, or Independent Party, in recent decades in Arkansas, Connecticut, Delaware, Florida, Hawaii, Louisiana, Maryland, Minnesota, Mississippi, New Mexico, New York, North Carolina, Oregon, South Carolina, Utah, and Vermont.
Parties in which the word “Independent” or “Independence” is, or was, part of a two-word party name have been: Alabama Independent Democratic Party (which placed Hubert Humphrey on the 1968 ballot); the Alaskan Independence Party; the Independent American Party in Colorado, Nevada, New Mexico, and Utah; the Independent Democratic Party of Georgia; the Independent Republican Party of Illinois; the Green Independent Party of Maine; the Independent Voters Party of Massachusetts; the People’s Independent Party of Nebraska; and the Virginia Independent Party.