By default, the names of your Android devices that appear for selection on the map screen of the Android Device Manager app will be the generic product name. However, if you would like to change this to something a little more personal then this can be done from within the app.
First, tap on the Menu icon (three dots) in the topright corner of the screen and then choose the ‘Rename device’ option from the menu that appears. You are then able to enter a new name for the device within the field provided. Once you have done this and are happy with the new name, tap on the Rename option and the new name will instantly be applied to your device when you select it from the main map screen in Android Device Manager.