Joking aside, the whole reason I named the car as I have is because there is provenance to that. The original cars from 2016, built to order by the 'factory' are more desirable than any other (presumably because people think they will be better built than by a bloke in his garage).
The manufacturer also has a very good reputation in the 'replica' industry, as their bodies were made to a very high standard and were dimensionally very accurate. So using the 'correct' name for the car means, IMO, everything is in order. Which will hopefully mean the car is more desirable.
If a 'kit car' is not registered correctly, ie if it's a Cobra rep but has Jaguar XJ6 on the V5, it can kill the value. When a kit car is for sale on any forum or facebook page, the first question is always "what is it registered as?"