Not all the time, but I've owned or been the principal driver of three named vehicles.
The first was an early-70s Dodge Dart which had a V-8 318 engine (as opposed to the slant-6 we'd expected). As it was old, ugly, green, but very powerful, we called it "Yoda".
The second was the car that I owned from 1990 through about 2001, a red VW Diesel Rabbit, which survived just about everything the world could throw at it until finally rust started getting to the superstructure. That was called "The Gratan", after the huge red omnienvironment vehicle seen in the anime Nadia: Secret of Blue Water.
My current vehicle is a 2002 green Impreza which is named "Virigar" after the villain in Digital Knight, mainly because it has that as its custom license plate.