As part of your offer, you may require a termite and pest inspection. This company not only inspects for termite damage and pest infestations, but also inspects for dry rot and water damage, among other things. The company that performs the inspection is important to you as a buyer, because you want to be sure they do a good job. It is important to the seller because it is customary that they pay for the inspection and some types of repairs that may be required.
You should determine which company you want to perform this inspection and make it a part of your offer. Otherwise the seller will choose. If you do not know which company to hire, your agent will make a recommendation.