current.json

{
	"_embedded": {
		"parent": {
			"_links": {
				"self": {
					"href": "/divisions/b76de4be-d59e-4562-b99c-78dafd04eef2"
				}
			},
			"id": "b76de4be-d59e-4562-b99c-78dafd04eef2",
			"name": "Parent",
		}
	},
	"_links": {
		"parent": {
			"href": "/divisions/b76de4be-d59e-4562-b99c-78dafd04eef2"
		},
		"self": {
			"href": "/divisions/eb336846-faa9-49f2-b99c-dc811b0a2fbd"
		}
	},
	"id": "eb336846-faa9-49f2-b99c-dc811b0a2fbd",
	"name": "Child"
}

desired.json

{
	"_links": {
		"parent": {
			"href": "/divisions/b76de4be-d59e-4562-b99c-78dafd04eef2"
		},
		"self": {
			"href": "/divisions/eb336846-faa9-49f2-b99c-dc811b0a2fbd"
		}
	},
	"id": "eb336846-faa9-49f2-b99c-dc811b0a2fbd",
	"name": "Child"
}

Division.php

<?php

declare(strict_types=1);

namespace App\Entity;

use ApiPlatform\Core\Annotation\ApiProperty;
use ApiPlatform\Core\Annotation\ApiResource;
use Doctrine\ORM\Mapping as ORM;
use Ramsey\Uuid\Uuid;
use Symfony\Component\Serializer\Annotation\Groups;

/**
 * @ApiResource(
 *     collectionOperations={
 *         "get" = {"method" = "GET", "path" = "/divisions/", "normalization_context" = {"groups" = {"division"}}}
 *     },
 *     itemOperations={
 *         "get" = {"method" = "GET", "path" = "/divisions/{id}", "requirements" = {"id" = "%uuid_regex%"}, "normalization_context" = {"groups" = {"division"}}}
 *     }
 * )
 * @ORM\Entity
 */
class Division
{
    /**
     * @var Uuid
     *
     * @Groups("division")
     *
     * @ORM\Id
     * @ORM\Column(type="guid")
     * @ORM\GeneratedValue(strategy="NONE")
     */
    protected $id;

    /**
     * @var string
     *
     * @Groups("division")
     *
     * @ORM\Column(type="string")
     */
    protected $name;

    /**
     * @var Division
     *
     * @ApiProperty(readableLink=false)
     * @Groups("division")
     *
     * @ORM\ManyToOne(targetEntity="App\Entity\Division", inversedBy="children")
     */
    private $parent;
}