Most cars have their brand/model number labeled on the car in a way, through various styles. I don’t know how much this would be to do because as far as I know all the badge assets are fixed right now but imagine a badge that automatically changes itself to be the name or brand or sub-trim of your car (user selectable so you can use more than one at a time). Have a couple font styles so you can do some differentiation but other than that you have a basically unlimited number of badges that could be procedurally generated from a font.
As you’re trying to design/make a car this seems like it could be an important part of the character to really make it your own.
Yes, and no. There is a mod (found under exhausts in steam workshop) for making your own badges, but they are frustrating to line up and only come in one style. There are also a couple of badges similar to the “turbo” badge pictured above for quattro and the like. But, as titleguy has suggested, this is not something likely to be implemented by the game at large. It would be something done by a modder (as is the case with the previously mentioned exhaust badges), so likely very limited in styles. Bottom line, work with what you’ve got or make a mod to give yourself something more with which to work.