Yup, you can buy a car on your name. But you'll need a Philippine drivers' licence. As long as your current drivers' licence hasn't expired, written and practical drivers' tests will likely be waived. You also shouldn't have any problems getting car insurance as a foreigner.
The main stumbling block might be financing the car, depending on your position. Are you going to pay for the car in cash? If yes, it should be a fairly easy process. If not, you might find it hard to get the car financed as most foreign banks won't grant a loan or credit facilities to foreigners.
Check out the Expat Arrivals Transport and Driving in the Philippines page as well for a few tips - it's not the easiest place to drive in!