Depends on the reasons why you would want to know. If for example you believe that this vehicle hit your car you can report it to your insurer. They will be able to apply to the DVLA for the owners name and address. If you think the owner of that vehicle might have broken the law (eg: didn't report an accident then the police will contact DVLA for relevant info).
You can always try contacting the DVLA direct yourself and see if they will give you this info (unlikely as it will be covered by the Data Protection Act).