How New Deal statists-turned-totalitarian fascists ended up with the title "liberal" is a mystery to me. It sure as hell ceased being accurate, if it ever was.
Yes, Hayek and Albert Jay Nock always called themselves liberal, too. The New Dealers co-opted the term. By the time a true liberal like Robert Taft came to prominence, was branded as a “conservative”, since he opposed the New Deal conception of the state.