I'm getting tired of telling people that the W is NOT the Westin. What is the origin of the "W" hotel's name?

A conversation often goes like this:

they say: "where'd you stay while out of town?"

I say: "A real hip, comfortable, cool hotel called the W"

They say: "Yeah - I stayed at a Westin once and it was real nice"

I say: "NO! It's not Westin, it's just W!"