Can a car rental company specify a brand when buying a car?

You can't.

According to the Notice of the Central State Organs on Fixed-point Purchase of Vehicle Leasing (Trial), the brand and model of the vehicle shall not be marked in the procurement documents, and even the service items are not allowed, so the car rental company cannot specify the brand to purchase the vehicle.

According to the sixth paragraph of Article 20 of the Regulations for the Implementation of the Government Procurement Law, restricting or designating specific patents, trademarks, brands or suppliers is a kind of differential treatment or discriminatory treatment for suppliers under unreasonable conditions.