Apologies, because this will probably come off rather dickish, but...
WA-167 between Puyallup and Renton is known locally as the "Valley Freeway".
Are you certain this is a nickname and not the actual name? I know the parallel surface street (part of which is SR 181) is officially the "West Valley Highway", and I think the freeway was named for the surface street. (In fact, a common error is to refer to 167 as the West Valley Highway instead.)
I-90 over Snoqualmie Pass is almost always referred to as "Snoqualmie Pass" (i.e. the road is the pass).
Is this not the case with most passes, at least those where the name is commonly known? Certainly is with nearby Stevens Pass as well.
I've also noticed a trend locally to refer to roads with the definite article. It's far from widespread but sometimes the traffic lady will slip and call it "The 90" but then follows with "Or...uh...I-90. Sorry".
If it's "far from widespread", then I don't think you can call it a "trend locally". In fact, that's how you tell the SoCal transplants from the homegrown locals. (Full disclosure: I am neither.)