Once the new name is selected, that is what will appear in the Play Store. You’ll then see the new name assigned to that piece of hardware. Give your devices an easy-to-remember name inside of Play. You’ll see the new title from the dropdown list when you install a new app.
You’ll see the new name when you go to install an app from the Play Store. Any time you want to change the name of a device. Even when you get a new phone and want to give it a name that’s easier to identify.