Can two different App with the same name exist in App Store?
No, the name of your app as it appears in the App Store must be unique.  When creating your app, you will receive the following error if you try to use a name that is already taken:


  The Application Name that you provided has already been used. Please provide a unique Application Name.


But the name on the icon can be whatever you want - it can be the same as another app's icon name.

Source: Quora