Now that I think about it, how does these names work in conversation? I mean when you talk to your friend do you just say "Well we can take Oscar" and then they are all puzzled because no one knows who Oscar is and you then have to break the awkward silence explaining that you thought it wise to give your car a name? How does that usually work for you?
Personally for me its like this "Lets take my car". Or when its me and my wife talking it will be "My kar of jou kar?" or "Die Corsa of die Astra?" Even in that conversation it will be silly if we gave the cars names because you refer to them by proxy of the regular driver or the type/make/model.