Yep ! should go back on its orignal reg..If you take it to a DVLA office you should get it all done in 5 days,
anyway its the dealers responsibility to do the transfer otherwise you can keep the private plate and
sell it back to him. Insure it on the reg that's on it now, and tell the insurance company that you are waiting
for the DVLA to assigne it its origanl plate and you will inform them when this happens, should be no charge.
Good luck with your new car...