Budget - Can I rent 2 cars, same time?

I will be flying with many family members (in the U.S.) and we'll need 2 cars. Can I rent 2 cars in my name at an airport location?
I might consider taking 1 car at airport and 1 car at nearby city (to avoid airport fees), is this OK? better? for both cars on my name (with extra drivers).

I rented two cars in Maui 2 years ago and Alamo. Since you can only drive one car at a time, the agent needed to rent the second car in the other drivers name with his identification. Airport locations are usually cheaper and more convenient to rent the cars.

book one at airport and one off site
it will save a lot of hassles and $$$ too

I've rented multiple cars before under my name, at the same time, same airport. (It was a large group). It was easier for the car rental people - having my info instead of setting up another customer, and more miles for me. A little weird maybe, but fine.