If my mom's boyfriend bought her a car as a gift and her name is on the insurance, can he report it stolen?

The main determinant will depend on whose name is on the cars registration and title. The items typically dictate "ownership" of the car. In Michigan, a person can be charged with a felony unlawfully driving away of a motor vehicle if they take a car without the "owners" permission. So yes, if the boyfriend meets these criteria, he can report the car as being stolen.