Answer: Como estructurar Switch Case en Dart?, a dartpad gist that have a method to navigate between pages written from textfield

navigate_to_page.dart

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        body: Center(
          child: MyWidget(),
        ),
      ),
    );
  }
}

class MyWidget extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => _MyWidgetState();
}

class _MyWidgetState extends State<MyWidget> {
  String _name = '';

  @override
  Widget build(BuildContext context) {
    return Center(
      child: Padding(
        padding: const EdgeInsets.all(16),
        child: TextField(
          decoration: InputDecoration(hintText: 'Ingrese nombre'),
          onChanged: (value) {
            setState(() {
              _name = value;
              print(value);
            });
          },
          onEditingComplete: _navigateToPage,
        ),
      ),
    );
  }

  _navigateToPage() {
    Widget destination;
    switch (_name) {
      case 'asesor':
        destination = AsesorPage();
        break;
      case 'asesorz':
      default:
        destination = AsesorzPage();
    }
    Navigator.push(
      context,
      MaterialPageRoute(builder: (_) => destination),
    );
  }
}

class AsesorPage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: Center(
        child: Text('asesor'),
      ),
    );
  }
}

class AsesorzPage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: Center(
        child: Text('asesorz'),
      ),
    );
  }
}