They didn't "get labeled"--they labeled themselves. Twice.They labeled themselves "socialists", and outside of America that was sufficiently deceptive to sell the concept. In America, we-the-people may not have articulated it this way, but we knew that it wasn't "social" at all--it was all about government power. Not "social"ism but governmentism--tyranny.
Here "socialism" became a terrible brand. Here "liberal" was what we-the-people actually were. So, having journalism on their side, the socialists simply redefined the term "liberal" to mean the opposite of its dictionary definition. And that was an accomplished fact in the New Deal era.
I think it is most properly denoted as a socialism via national government enforcement, or more simply "National Socialism"--this also gives it the approriate conotation.