I have just made an iOS app that can share to Facebook. The Facebook post correctly shows that my sharing is coming from my app and shows \"1 hours ago via MYAPP\". The name of
In "Native iOS App" on your Facebook app settings just enable "Deep Linking". This would make facebook check if the app exists (probably by checking "canOpenURL" with your app URLScheme) if it exists it would open your app and if it doesn't it would send your users to iTunes.
Pay attention it could take a while till this change would be propagated.