Do I need to name all the drivers when we rent the car?

Usually yes. Most of the companies have a clause that if someone driving is not mentioned then you will loose the insurance. At least it is the case with the international ones in Thailand. Local rental companies I do not know.

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Yes, this is required by renting and insurance policies. If you don't name some-one, and he/she makes accident the insurance handling is not same and of course worse for you.

I guess it's not a big deal at all to name the drivers and guess also you don't want to make a random driving with the rented car.