Maybe from French trappers?

Reminder that the capital of Idaho, Boise, is (apochraphally) named for the trees (les bois) that surround the Boise river. French made it quite a ways west, and definitely made it as far as Idaho.

The story goes Owyhee County is named after Hawaii. It's a county southwest of the Boise Area and home to the most beautiful wilderness I have ever seen. There is nothing like hiking mile after mile out there under the hot summer sun never seeing another living soul... But I digress. The story goes some Hawaiian goat herders entered the area to try their luck and were never to be seen again and hence the name. Owyhee = Hawaii How true it is I do it know but it's what I've always been told.

https://en.wikipedia.org/wiki/Owyhee

And the Tetons in western Wyoming / eastern Idaho.

French trappers. Supposedly the name means "heart of an awl" regarding the shrewd business practices of the local native tribes.

The annual rendevous was held in Idaho. There are quite a few French named things around the area. Lake Pend Orielle, etc.

Also, lots of stuff named after Lewis and Clark, the Jesuit priests and the Mullan trail.