All RM vehicles, some racing models (such as the Citroen GT Race Car), Stealth models, Racing Karts, and some DLC race models can have their numbers changed. None of the standard models can have their number changed.
The vehicle in the picture, as stated before, are the Renault Sport Clio/Lutecia Trophy Cars. These cars are standard models and come with a variety of liveries, with each livery having their own unique number. Other cars that share this behavior are the Lupo Cup Car, Lupo GTI Cup car, New Beetle Cup Car, Mazda RX-7 Super Touring Car, Toyota Altezza Super Touring Car, Subaru Impreza Super Touring Car, and others. These numbers can not be changed.
Other examples of standard cars that have different liveries with different numbers are the Dodge Viper GTS-R Team Oreca (51, 91) and the Audi R8 Race Car (1, 2). These models can not have their number changed.
If a car can have its number changed, it is displayed in the garage with a "99" icon along with the standard icons (description, demo, sell, get in, info, cancel, etc.) when viewing the vehicle.