Iirc the Nation's Cup allows you to drive any car you have and custom liveries are allowed. The Manufacturers Cup forces you to use only the car the manufacturer loaned you which cannot be customised.
Just change into your hire car, go into Home and use the Change Livery button to apply an existing livery for that model, or if you want to make a new one, you can now pick the hire car in the Livery Designer.
Just change into your hire car, go into Home and use the Change Livery button to apply an existing livery for that model, or if you want to make a new one, you can now pick the hire car in the Livery Designer.