There is no way to remove www or control how your URL will show up in your ads. It used to be that you could but not anymore, for almost two years now in fact and is a sore point with many advertisers. Google claims that having the www in front and the domain all in lower case increases the click rate. I and others question this. It may be done just so ads look more like the SERPs and thus blurring the distinction between ads and organics.
#1 On your actual site are all requests for "www." forcibly redirected to the without-www form?
#2 In gwt have you verified both versions (yes, it sounds stupid, but you have to) of the site, and set the preferred form to "without www"?
If you've done both of those, then you can safely say that "www." exists nowhere but in g###'s fevered imagination, and file it in the same mental compartment as those "crawl errors" that you can only ignore. When your advertising draws people to your site, they'll end up on the name you want, no matter what g### sees fit to call it.