Did they ever mention Volkswagon?

That I recall, Volkswagen was never mentioned in this film I believe you're correct regarding the insignia as well, although it did become visible/more prominent in subsequent films as I recall.

The name "Beetle" by the way, is a direct translation of the German word Käfer. As you say, the car was officially a Type 1, but there's nothing much cute or endearing about that designation.

Bug, Superbug, etc., evolved from Käfer, though.

I believe it was because they never got permission from Volkswagen to use the name. Whether this was intentional, or an oversight, I don't know. I'm sure Disney could have afforded to pay for the right to use the name, and I would think Volkswagen would have liked the publicity.

I think the use of the phrase "the little car" worked better than using the actual name. It was more of an endearing term that fit the character of Herbie perfectly.

I know they did at least once -- in Herbie Rides Again, Stephanie Powers referred to the car as a Volkswagen when they were floating along in the bay. Only reason it sticks in my head was because she pronounced it VolkswAHHgen.

It's interesting that Mr Wu says that Herbie has 'the power of 40 horses' after Herbie revives for the second half of the last race. This is the same power as a VM Beatle with a 1.2ltr engine, but yeah, they never mention VM or Beatle throughout the movie.

They don't need to call it a "Volkswagen" because everyone and his dog already knows it's a Volkswagen. It's like saying why doesn't Steve McQueen or anyone else in "Bullitt" call the car he drives a "Mustang." Everyone and their cat already knows it's a "Mustang," since that was a very popular car model and still is, even if only car-buffs know it's a 1968 Ford Mustang 390 GT 2+2 Fastback.

The Volkswagen Beetle or "Bug" as designed by Hitler himself at a Munich restaurant in 1932 (see authenticated drawings at link below) and eventually finished by National Socialist Workers Party and Waffen-SS member Ferdinand Porsche, was already, by the 1968 release of the "Love Bug," the most popular & longest lasting car model of all time. It eventually sold over 200 million units by the time the original model, albeit with many improvements over the years yet nothing changed in the basic design, was retired in the 1990s. The immense popularity of Porsche's final original design is even more impressive when you realize that the Beetle was built at a time when only 35 out of a thousand Germans could afford the 5 marks a week to buy one to drive on the first and still greatest autobahn-freeway ever built.

http://www.hitler.org/artifacts/volkswagen/

In addition, as anyone with the slightest interest in automobiles knows, the VW Bug was the pre-cursor to the Porsche 911, another very popular car (maybe the most famous sports-car in the world), whose basic design also did not need to be changed for many decades, only improved upon in non-foundational ways.

Last but not least, the single most popular musical group of all time was named "The Silver Beetles" before they became the "Beatles" (notice the one letter change). Coincidence? I think not. I've got my own theory. They wanted popularity, so they picked a name that was already on everyone's tongues, that also "just happened to be" that of the most popular car around. "Silver" was probably just added to keep from being too obvious. A little later, the change from Beet to Beat-les still kept the sound of what Hitler's "people's car" was called by the English-speaking world but imposed a spell-ing on people that suggested rhythm (beat) and beatnik culture (eccentric artsy-fartsy pre-hippie "hipsters" of the 1950s and early 1960s).

https://www.youtube.com/watch?v=63_BMNxTces

https://www.youtube.com/watch?v=6zA5nLp8AS4