With the classes you have shown us here, there is nothing shorter than
Person p2 = Person()
  ..name = p1.name
  ..surname = p1.surname
  ..city = (City()..name = p1.city.name..state = p1.city.state);
If you add a clone method to Person and City, then you can obviously use that.
There is nothing built in to the language to allow you to copy the state of an object.
I would recommend changing the classes, at least by adding a constructor:
class Person {
  String name;
  String surname;
  City city;
  Person(this.name, this.surname, this.city);
}
class City {
  String name;
  String state;
  City(this.name, this.state);
}
Then you can clone by just writing:
Person P2 = Person(p1.name, p1.surname, City(p1.city.name, p1.city.state));
(And ob-link about names)
I say that there is no language feature to copy objects, but there actually is, if you have access to the dart:isolate library: Sending the object over a isolate communication port. I cannot recommend using that feature, but it's here for completeness:
import "dart:isolate";
Future<T> clone<T>(T object) {
  var c = Completer<T>();
  var port = RawReceivePort();
  port.handler = (Object o) {
    port.close();
    c.complete(o);
  }
  return c.future;
}
Again, I cannot recommend using this approach.
It would work for simple objects like this, but it doesn't work for all objects (not all objects can be sent over a communication port, e.g., first-class functions or any object containing a first class function).
Write your classes to support the operations you need on them, that includes copying.