Quoted from Bryan_Kelly:From google.
The Three Dog Night Story, 1964–1975 states that vocalist Danny Hutton's girlfriend, actress June Fairchild (best known as the "Ajax Lady" from the Cheech and Chong movie Up In Smoke) suggested the name after reading a magazine article about indigenous Australians, in which it was explained that on cold nights they would customarily sleep in a hole in the ground while embracing a dingo (wild dog). On colder nights they would sleep with two dogs and, if the night was freezing, it was a "three dog night".
Yes!