The name on the store, and my gf's paycheck, is "NORDSTROM". In fact, these days, it's always in caps. It was originally a shoe store. I dunno if the store name was ever possessive, though I believe it is the name of the founder. EDIT: I'm dumb as a post, you didn't ask which it was. I say both, but then, I've already demonstrated my lack of observational skills.
Yes, name of founding family (though I don't know if privately owned, or if family still controls stock). They're from Washington State I believe.