I'll just open this jag-jar full or worms
After building you have a RADICLY ALTERED VEHICLE.
The V5 detail, make and model, are wrong and must be changed to read correctly, you responsibility.
Your insurance will not pay out if the V5 is wrong, part of the insurance form says "any alterations or modiforcations" "
If you vehicle is tax exempt them obtaining a tax disc with a incorrect V5 is technically fraud so your tax is also invalid.
My advice is you NEED to inform your insurance company and the DVLA.
Of course, at the end-of-the-day you can just do what you want. You just hope PC plod "knows nothing"