The designated driver in a group of people travelling together is the one who has agreed to drive, or who is insured to drive.
designated driver in British English
noun
a person who volunteers not to drink alcohol on a social occasion, so that he or she can safely drive other people who have been drinking
designated driver in American English
the person in a group who has been designated as the one who will abstain from alcoholic beverages so as to be able to safely drive the others in a motor vehicle