It's a very expensive process, but all you need to do is go to the traffic department in madinat khalifa and request the numberplate of your choice, and once you pay for it your car can be changed over to that number.

Although it's a good idea first to see if the number you want is taken, which you can do by checking www.moi.gov.qa, just search the traffic violations, and you will see if the numberplate is already in use.

Good luck!