The day before departure, I received a WhatsApp message from the car rental company confirming the drop-off location. If there were any issues, I could reply to them immediately.
After placing the order, following Klook's instructions, go to the 2nd floor of the BKK departure/arrival level, between gates 4 and 3. There is a blue ❓ counter opposite the AOT Airport Information desk. Look for your car rental company's sign or ask the staff. The company sign has the customer's name attached to it (I didn't choose the free name sign option). The staff will verify the order, take a photo of you, and then contact the driver. Once the license plate number is available, they will provide it to you, tell you which floor and gate to go to, and how long to wait for boarding (though I feel you can also ask for the car's color just to be sure).
After getting into the car, the driver was very polite and helpful, automatically helping to load our luggage. The interior of the car was neat and clean, and the driving was smooth and safe.