It’s important when customers look for your app on their devices that they immediately recognize its icon and name, just as they appeared when the user downloaded your app from the store.
There are various creative ways to design your App Store icon so that it is similar to the icon that will be displayed on a user’s device—one technique for instance is to present a close-up of a specific icon section—but whatever approach you take, make sure the small icon retains a very similar look to the large one.
Similarly, you should create a name for your app that will be consistent with what customers see on the App Store and how it appears on their device. If your app’s name in iTunes Connect is, for instance, “Coraline’s Creative Cajun Cooking,” good choices for short names for devices might be “CreativeCajun,” or “CajunCooking” or “Coraline’s,” which directly evoke the long name, but not “Good Eats,” “Louisiana,” or “Comfort Food,” which do not.
The golden rule is simply that an end user should instantly associate the name and large icon in the iTunes App Store with the name and app icon on their devices.