Sorry to be pedantic as this is often incorrect: King county was NOT named after MLK Jr, but rather changed recently from referring to Rufus King to MLK Jr. I had mistakenly believed this too before I learnt about our history.
But Washington State is indeed named after George Washington.
It's no accident you assumed that. King County Metro uses MLK as their logo, so you can't even walk a block downtown without seeing a 10-ft mobile billboard of MLK's face.
Another tidbit I learned today: S Jackson Street (running through the International District in Seattle) is, in fact, named after President Andrew Jackson.
But Washington State is indeed named after George Washington.