I've never given a vehicle an actual name, although they occasionally get nicknames.
My truck is just "the truck". My wife's car is "the Audi". Our daughter's car that stays out our house is "the Subaru" or "the Suub". My car is "the Corvette" or Vette, sometimes "the baby" because the first time my wife drove it apparently I had such a look on my face she said "Don't worry, I'm not going to drop the baby!". So now if I'm going to the carwash "the baby is getting a bath", if I'm putting it in the garage I'm "putting the baby to bed".
Years ago we had a truck we called "the Bomb". It was a mid-70s Ford HD truck, rattle canned blue, not a straight panel on it, and I-beams welded on for bumpers. As you drove it, people noticeably moved away from it on the road and gave you plenty of room. Just as if the truck had "DANGER! BOMB ON BOARD".