What they had was (Leninism-)Stalinism.
It really had nothing to do with communism, except that it sounds better to say "we have communism" than "from now on I'm your dicktator, suckers".
It's called branding.
The same thing that makes Ford claim a car is fuel efficient because it uses 21 mpg.
"The first thing Fascists usually try to do is silencing the opposition."
