updating variable changes in components from a service with angular2

Provide an event in the service and subscribe to it in the components:

@Injectable()
class NameService {
  name: any;
  // EventEmitter should not be used this way - only for `@Output()`s
  //nameChange: EventEmitter<string> = new EventEmitter<string>();
  nameChange: Subject<string> = new Subject<string>();
  constructor() {
    this.name = "Jack";
  }
  change(){
    this.name="Jane";
    this.nameChange.next(this.name);
  }
}

export class SomeComponent { 
  constructor(private nameService: NameService) {
    this.name = nameService.name;
    this._subscription = nameService.nameChange.subscribe((value) => { 
      this.name = value; 
    });
  }

  ngOnDestroy() {
   //prevent memory leak when component destroyed
    this._subscription.unsubscribe();
  }
}

See also
angular.io – COMPONENT INTERACTION – Parent and children communicate via a service