In order to change your name in AirDrop in iPhone, you need to alter the device name. Go into Settings > General > About and tap Name. Insert the new name you desire to type. This name is your AirDrop name. So in case you, are asking yourself how to rename AirDrop or how to change AirDrop name, this is how you do it. It is minute and it works with every iPhone. Upon saving, other people will get to view your new name on AirDrop.