Idaho County, Washington Territory was created on December 20, 1861. It was named after the steamboat Idaho. You might have missed that because that county ended up in the new Idaho Territory in 1863 when the boundaries were drawn. Nez Perce and Shoshone counties were also originally counties in Washington Territory for a short time.
If you want to step back a few years, all of you living in Idaho today would have been living in either Walla Walla County, Washington Territory, or Skamania County, Washington Territory. They were created in 1854. The former included all of present day Idaho above the 46th parallel, and the latter the rest of it.