The pushNamed method also accepts arguments, to pass to the new Route:

Navigator.of(context).pushNamed('/2', arguments: "Hello from screen 1");

In this case, we need to use onGenerateRoute from WidgetsApp so that we have access to these arguments through the RouteSettings object:

// navigation_widgetsapp_named_routes_arguments.dart
class _NavigatorNamedRoutesArgumentsAppState
    extends State<NavigatorNamedRoutesArgumentsApp> {
  @override
  Widget build(BuildContext context) {
    return WidgetsApp(
      color: Colors.blue, 
      onGenerateRoute: (settings) {
        if(settings.name == '/') {
          return MaterialPageRoute(
            builder: (context) => _screen1(context)
          );
        } else if(settings.name == '/2') {
          return MaterialPageRoute(
            builder: (context) => _screen2(context, settings.arguments)
          );
        }
      },
    );
  }
  ... 
}

After that, we use the argument normally found in in the _screen2 builder, to display an additional message.