User (id, name, department_id)
Department (id, name)

+----+-------------+--------------+
| id | name        | department   |
+----+-------------+--------------+
| 1  | User 1      | 1            |
+----+-------------+--------------+

+----+-------------+--------------+
| id | name        | department_id|
+----+-------------+--------------+
| 1  | User 1      | Department 1 |
+----+-------------+--------------+

User.php

public function _department() {
    return $this->belongsTo('AppModelsDepartment','id');
}

Department.php

public function _user() {
    return $this->hasMany('AppModelsUser','department_id');
}

class UserCrudController extends CrudController
{
    public function setup()
    {
        /*
        |-----------------------------------------------------------------------
        | CrudPanel Basic Information
        |-----------------------------------------------------------------------
        */
        $this->crud->setModel('AppModelsUser');
        $this->crud->setRoute(config('backpack.base.route_prefix') . '/user');
        $this->crud->setEntityNameStrings('', 'User');
        $this->crud->allowAccess('list');

        /*
        |-----------------------------------------------------------------------
        | CrudPanel Configuration
        |-----------------------------------------------------------------------
        */
        $this->crud->addColumns([
            [
                'name' => 'id',
                'label' => "ID",
                'type' => 'text',
            ],
            [
                'name' => 'name',
                'label' => "Name",
            ],
            [
                'name' => 'department_id',
                'type' => 'text',
                'label' => 'Department',
                'entity' => '_department',
                'attribute' => 'name',
                'model' => 'AppModelsDepartment'
            ],
        ]);

        $this->crud->setRequiredFields(StoreRequest::class, 'create');
        $this->crud->setRequiredFields(UpdateRequest::class, 'edit');
    }

    public function store(StoreRequest $request)
    {
        // your additional operations before save here
        $redirect_location = parent::storeCrud($request);
        // your additional operations after save here
        // use $this->data['entry'] or $this->crud->entry
        return $redirect_location;
    }

    public function update(UpdateRequest $request)
    {
        // your additional operations before save here
        $redirect_location = parent::updateCrud($request);
        // your additional operations after save here
        // use $this->data['entry'] or $this->crud->entry
        return $redirect_location;
    }
}