The Nazis were originally called the German Workers Party, and the name change to incorporate the word "socialist" was partly designed to pull in working class voters by making the party seem more caring and respectable than it actually was, because "socialism" was a relatively "good" word to many idealistic people in the 1930s on both sides of the Atlantic.

But in any case, merely because a party calls itself by a name doesn't mean that this is what it stands for, and that is especially so given the low standards of honesty practiced by totalitarians.

Vladimir Zhirinovsky's Russian fascist group of the 1990s was ludicrously called the Liberal Democratic party although it was virulently anti-liberal and anti-democratic.
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The only people pushing the Athenian Straw Man Nonexistent Threat of Slippery Slope Windyfoggery (ASMNSSW) RE DEMOCRACY are people who have a misunderstanding/problem or hatred of democracy. (See AUTHORITARIANS)