You can use Parkster with a personalized licence plate. Simply enter the licence number that appears on the licence plate.

Identification mark
Once you have paid for your personalized licence plate, the Swedish Transport Agency will send new licence plates and an identification mark. 
 
The identification mark contains the vehicle's regular registration and identification marking (chassis number), as well as the designation of the personalized plate. The mark must be present on the vehicle in order to use the personalized plates. It should be placed on the rear right side window of the vehicle. If this is not possible, it should be attached to another location where it can be easily read.

On the Swedish Transport Agency's website, you can read more about the requirements for owning a personalized licence plate.