Finally I found another way (from another forum) which is working!
I share it with you may be someone will be interested.
Following same idea, a simpler solution might be just including hidden inputs with values in com_users\views\registration\tmpl\default.php above
<button type="submit" class="btn btn-primary validate"><?php echo JText::_('JREGISTER');?></button>
add
<input type="hidden" id="jform[username]" name="jform[username]" value="username" />
<input type="hidden" id="jform_name" name="jform[name]" value="name" />
It would pass the validation and you would no longer need to override controllers etc.