Personal Reg Plates
You can indeed have your personal reg plates on your lease car. However, Legal Vehicle Services are unable to facilitate this change. To do so, speak with your finance company as soon as the deal is confirmed who will then assist you via the DVLA to get the plates changed.
Because the finance company have the logbook and they are the registered keeper/owner, this can not be done by yourselves but it still a very simple process.
If you have your private registration number on a retention or purchase certificate, you will need to add your leasing company to the "Nominee" section