Is naming “Ormendahl, Profane Prince” a legal choice for Infinite Obliteration, given that Westvale Abbey is a non-creature? If so, what happens on resolution? I'm assuming you search for Ormendahls, find a lot of Westvale Abbey's instead, and nothing ends up exiled.

Your assumption is correct.

It's legal to name Ormendahl, Profane Prince for Infinite Obliteration, but it won't help you very much, because all you'll see when you go searching for cards with that name is a bunch of cards named Westvale Abbey. Since the name “Westvale Abbey” isn't the same as the name “Ormendahl, Profane Prince”, you won't end up exiling anything, and you'll have wasted your Obliteration.