Thank you for your question.
To the extent that the car was damaged while rented under your name, you personally will be held financially responsible for paying the damage. To the extent that a new car is rented on a debit card, the facility can take a deposit. (Some rental agencies take deposits of $200-$300 when a debit card is used to secure the rental and any potential damage to the rental.)
Unfortunately, without listing your boyfriend as an additional driver, he had no legal ability to drive the vehicle. As such, you can be held financially responsible for all dealings with the vehicle.
To contest any of the charges, you will need to know every line item that is being charged by the company in order to assess its validity.
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