Hardcastle and McCormick Coyote x
Always wanted the Jupiter 8 from planet 892-IV:
In Rex Stout’s Nero Wolfe series (and Robert Goldsborough’s sequels), Archie drives Wolfe’s Heron sedan. He drives more than one model through the years.
Stout liked making up brands for his books – Heron sedan, Marley pistols, the names of the locks. Goldborough kept up the tradition, inventing “Cherokee” sodas, instead of using, say, Coke or Pepsi.
The Thorndyke Special from Herbie: The Love Bug. I’d always assumed it was a rebodied Jaguar E-Type but apparently it was an Apollo GT.
GM produced a bunch of “fake” cars for Demolition Man, and Rover Group did the same for the 1995 version of Judge Dredd like the City Cab 1. Not sure if those fit the OP’s criteria since they come from real companies.
In the Mr. Plow episode of The Simpsons, Homer test drives a car apparently called the “Harper Invacar” from Crazy Vaclav’s Place of Automobiles.
“Put it in H!”
As I remember, the cars used in Demolition Man were real GM concept cars, so the model and brand names (if any were specified in the movie) might have been fake, but the cars were sort of real.
A few were, such as the Ultralite, which was used as the SAPD police cruiser, but most were built specifically for the film.
The early 90s movie “Class Action” was about a car called the Meridian.
The comic strip “For Better or For Worse” had a character who sold a car called the Crevasse.
Since this is about brands in movies and TV, let’s move it to Cafe Society. Title edited to better indicate subject.
How about the Turbo Interceptor from 1986’s The Wraith.
According to IMDB it was in reality the Dodge M4S. A joint effort of the Dodge Division of Chrysler Motors and PPG Industries, one of the pace cars for the PPG-CART Indy Car World Series.
Hey, that’s a pretty cool looking thing.
King of Queens had a Douchenberger, made in Luxembourg. It’s the most popular car over there! I think it was actually a Mini.
The most infamous TV car: A 1928 Porter . . . 
Video games, there’s a wealth of fictitious makes/models between the Grand Theft Auto series, the Saints Row series and the Mafia games.
There was the Assan Motor Company in the movie Gung Ho.
Porter was a real brand. Hardly any made however and none by 1928. The car used in MMtC was a modified Model T.
Yeah, yo momma…
Designed by Chip Foose while he was still in high school.
That’s actually not a fake car. It’s a car manufactured by Manta. You can still get one if you look around and have the money, because while they were looked down on when they were new as junky kit cars they have quite a following now.