So, apparently they wanted to incorporate 3 in the name because they had 3 singers. At the time, they had a list of 60 possible names, but couldn't decide. Their manager said he wanted a name by Monday. About that time, the girlfriend showed him an article about Australian aborigines and a saying they had about bitterly cold nights, where they'd have to sleep with 3 dogs to be able to stay warm a.k.a. a 3 dog night.
That's all according to an interview with Danny Hutton, one of the founding members
P.S. first thing that popped in my head when reading the title too
Sunoverbeach wrote: