It usually depends upon state laws if a minor can title and register a vehicle in their name. Most states will allow a teenager under 18 to do so but there are a few that do not. If your granddaughter was able to register and insure a vehicle under her own name previously then it would appear that state laws should allow her to do so once again.
To find out for certain what your state allows in this situation, check with your state's Department of Motor Vehicles. Since your granddaughter is a minor it may be that a parent or guardian will need to sign any legal documents with her, such as the registration and insurance policy contract.
If you or your granddaughter is in need of insurance quotes, you can start here with us. If she is under 18, she will need a legal adult to sign her insurance contract.