Yes if you have liberty mutual car insurance on your own vehicle or vehicles then yes the liberty mutual car insurance you have on your own vehicle will be extended to a car rental.
But that is only for in the United States if you live in the United States and have Liberty Mutual Car Insurance and rent a car out of the United States then your liberty mutual car insurance will not extend to or cover your rental car.
When you rent a car from a rental company they will have car insurance on the car so you usually do not need auto insurance yourself when renting a car.
But having your own liberty mutual car insurance extended to the rental car is a good idea and Liberty Mutual is a wonderful car insurance company.