It's pretty much a given VW won't give its permission, if asked. At best they'd want final say over the book in which it is used. Google use of corporate logos in fiction/art, or something similar. If you don't ask and VW finds out, they may just ignore it, as long as it doesn't have a negative impact on VW.
If it's parody, then it's protected as free speech, as long as you don't mind dealing with lawyers. Some companies strictly defend their brands, otherwise the courts could eventually rule against them if everyone started doing the same thing.
In the 2001: A Space Odyssey movie, they featured Pan Am for ships that travelled into space, but that was a very different era, and it may have been a product placement. I don't know if Arthur C. Clarke used their name in his book. You might be able to google that too.
Originally, Lucasfilm tried to shut down many sites of fan work derived from Star Wars, even those that made no profit off their work. Fortunately for SW fans, George eventually caved and now the presence of SW on the Internet is everywhere, mostly positive.
Mikira could consider something like Vee UU, but parody may not be what she wants.
