A few months ago Apple sued Amazon by using the App Store name to refer to the application store for Android that had created. The Cupertino company claimed that the name was very much and that it was not a generic term.
The judge in charge of the case decided to not give it reason to Apple and considered that the App Store name is generic and that therefore he cannot exercise over it any judicial protection. Therefore Amazon can continue to use the name without any problem in your app store.
Now only that the trial be held, dated to October 2012, and the case is closed. We will see how to pass the rest of lawsuits that has Apple against other companies related to the world of as for example Samsung Android.