Renter's Insurance won't cover a garage structure, but it should cover personal property in a garage. If you own a garage you will likely need to buy a seperate policy for the building as Renter's Insurance doesn't include any coverage for structures. Hope that Help!
Chief Executive Officer, Coastal Homeowners Insurance Solutions, Rocky Point, NY 11778
Renters insurance is designed to cover your personal property (your stuff) and personal liability. It will not cover physical damage to a garage because you have no insurable interest (you do not own the garage). If you had personal property inside the garage and it was damaged or stolen from a covered peril you could make a claim. I'd suggest you reach out to your local independent insurance agent to discuss what your policy covers. Hope this answer helps.
Send me a message if you have more questions.