Check a few post down - titled Santo Domingo to Punta Cana, you will find good info on the buses, stops location, times, and cost to get you from west to east. I don't think there is an offoical name like "Carbie Tours" as it is explanied it is just a smaller bus .....same service. Hope this help in your search.
The bus to LaRomana can be boarded just next to Plaza Lama.
As your standing facing the front of Plaza Lama, go to the left and it's just to the right, I believe around the first corner is Asomiro and the second corner is sichoem. ( probably not spelled right)