MongoDB embedded subdocument mapping with a Symfony Form

Question

I'm trying to make a form who's populate a Mongo Database. I'm using Symfony Framework and the Doctrine ODM to achieve it. And There is my problem :

I would like that the FormBuilderInterface generates 3 form fields like :

<form>
    <input name="names[name]" />
    <input name="names[lastname]" />
    <input name="names[nickname]" />
</form>

And when the user submits the form, document in DB may be like :

"names": {
     "name": "James",
     "lasname": "Bond",
     "nickname" : "007"
 }

MongoDB V4.4.2 - Symfony V4.20.5 - PHP V7.4 - Doctrine/mongodb-odm-bundle V4.2

HERE IS MY PHP FILES :

Person Document (Entity)

//   src/Document/Person.php

<?php

namespace App\Document;

use Doctrine\ODM\MongoDB\Mapping\Annotations as MongoDB;

/**
 * @MongoDB\Document
 */
class Person
{
    /**
     * @MongoDB\Id
     */
    protected $id;
     /**
     * @MongoDB\Field(type="collection")        // !! Am I wrong ? ?
     */
    protected $names;    
}

The PersonType (Form builder)

// src/Form/Type/PersonType.php 

<?php

namespace App\Form\Type;

use App\Document\Person;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\Extension\Core\Type\TextType;
use Symfony\Component\Form\Extension\Core\Type\CollectionType; // !! Am I wrong ?
use Symfony\Component\Form\Extension\Core\Type\SubmitType;
use Symfony\Component\Form\FormBuilderInterface;
use Symfony\Component\OptionsResolver\OptionsResolver;

class PersonType extends AbstractType
{

    public function buildForm(FormBuilderInterface $builder, array $options): void
    {
        $builder
            ->add('names', CollectionType::class,        // !! Am I wrong ?
                    [
                     'entry_type' => TextType::class,
                     'allow_add' => true,
                     'by_reference' => false,
            ]);    
    }

    public function configureOptions(OptionsResolver $resolver){
      $resolver->setDefaults([
        'data_class' => Person::class 
      ]);
    }    
}

The Controller

// src/Controller/PersonController.php

<?php

namespace App\Controller;

use App\Document\Person;
use App\Form\Type\PersonType;
use Symfony\Bundle\FrameworkBundle\Controller\AbstractController;
use Doctrine\ODM\MongoDB\DocumentManager;
use Symfony\Component\HttpFoundation\Request;
use Symfony\Component\HttpFoundation\Response;
use Symfony\Component\Routing\Annotation\Route; 
    
class PersonController extends AbstractController {

    /**
    * @Route("/mongo/", name="mongo")
    */    
    public function new(Request $request DocumentManager $dm): Response {

        $person = new Person();
        $form = $this->createForm(PersonType::class, $person, []);

        //If form is submitted I know how to persist data. (with $dm->persist)
        //But problem is how to generate the form and then when It's submitted
        //the "names" field in my mongo db embed the fields lastname, name, and nickname
            
        return $this->render('dashboard/enrolment.html.twig', [
            'person_form' => $form->createView(),
        ]);   
     }
}