Yes, it is usually the car that is covered, not the name.
However, if you wish OP, you can simply call your insurance company and add her as a "part time driver." This may lead to a rate increase depending if she is a younger driver or has a claim history.
You only need to do this if her permanent address which is stated on her license is the same as yours. Usually insurance companies require all licensed drivers living in the same household to be included on the insurance policy unless they have their own separate insurance. They use the DMV datebase for finding out this information.
So as long as her address isn't the same as yours, you should be okay not including her, if something does happen, you will have to state you willingly gave her the keys and let her borrow the car temporarily. If she will be driving your car very frequently, you should probably add her as a part time driver under your policy.