I have never made up a name for any of the cars I've had. Lots of guys do, and I don't know why I never did it. (Oh, I've sometimes referred to my 46 as 'The Old Girl', but no real name. Didn't do it for my first car, a 62 Chrysler Newport, either.) However, for some reason, while driving home from a service call this evening I thought of a name for the 46 P15 - 'Cearense'. (It's the name for people from the Brazilian state of Ceara. It's fitting for a particular reason, but maybe there is someone here who can guess at the connection. (You almost have to be from there, or at least from Brazil.)
Another question, if you DO make up pet names for your cars, do you also have a pet name for your wife? Strange question, I know, but I also always just call my wife by her name, none of that "Sweety", or "Princess" stuff, and she has also always just called me by name. I don't know why, either. We knew a Brazilian couple who called each other "Meu Bem", which translates literally as "My Good".
(If no one can guess, I'll explain why I thought of Cerense as a name for the Plymouth. One hint: It still has an L-Head Six in it.)