There are many companies providing these services. We would stick to recommended companies and reasons why recommended.
Oryx 4x4 hire
Oryx is based right outside the Park gate and is thus ideal to book them to do a pick up at the airport to the Lodge and hire a 4x4 to drive in the Kgalagadi Park. There is a wide variety of vehicles including 4x4s required for some places in the park, combi and SUV,s