I will tell you the main part where you should change this.

// add this extra field
$table->string('username');

In the register blade, you should add a username field also so the user can choose the email or username that he should use for login. I skip that and go to the login method.

<!-- replace this email field with login -->
<input id="login" name="login" type="text" class="form-control">
 

In LoginContoller here is an update code below. You find this controller in app/Http/Controllers/Auth

<?php
 
namespace App\Http\Controllers\Auth;
 
use App\Http\Controllers\Controller;
use Illuminate\Foundation\Auth\AuthenticatesUsers;
 
class LoginController extends Controller
{
    /*
    |--------------------------------------------------------------------------
    | Login Controller
    |--------------------------------------------------------------------------
    |
    | This controller handles authenticating users for the application and
    | redirecting them to your home screen. The controller uses a trait
    | to conveniently provide its functionality to your applications.
    |
    */
 
    use AuthenticatesUsers;
 
    /**
     * Where to redirect users after login.
     *
     * @var string
     */
    protected $redirectTo = '/home';
 
    /**
     * Login username to be used by the controller.
     *
     * @var string
     */
    protected $username;
 
    /**
     * Create a new controller instance.
     */
    public function __construct()
    {
        $this->middleware('guest')->except('logout');
 
        $this->username = $this->findUsername();
    }
 
    /**
     * Get the login username to be used by the controller.
     *
     * @return string
     */
    public function findUsername()
    {
        $login = request()->input('login');
 
        $fieldType = filter_var($login, FILTER_VALIDATE_EMAIL) ? 'email' : 'username';
 
        request()->merge([$fieldType => $login]);
 
        return $fieldType;
    }
 
    /**
     * Get username property.
     *
     * @return string
     */
    public function username()
    {
        return $this->username;
    }
}

If you need more about it here is the link