In a nutshell, no.
You can rent a car and list a second driver. You will still need to sign the contract, and pick up the car but then you can give it to whomever the second driver is.
If you are trying to rent a car for someone who is not in the same city as you, then the simple answer is no. You may be able to have the person rent the car themselves and offer your credit card as a guarantee of payment if they don't have one of their own.
In either of the above scenarios, you remain responsible for the vehicle and if it gets totaled, you just bought it.
Since this is DR1 we must be talking about renting a car in the DR. For enough cash, you can probably do anything you want. Might be cheaper to buy this person a second hand car though.