Custom error for user registration page in D7 not working
The reason why it's not displayed are:


Since the field is required, Drupal handles that already so your user-defined validation wouldn't run since Drupal make's sure the field passes "required" validation and when it reaches your trapping, it's never empty.

  First ensures required fields are completed, #maxlength is not exceeded, and selected options were in the list of options given to the user. Then calls user-defined validations.


Reference: function _form_validate


Here is an example that your functions are right.

if ($form_state['values']['name'] == 'asdasd'){
    form_set_error('name', t('username is asdasd!'));
}


That will trigger your validation since it passes the "required" validation and checked the username for something aside from being empty which conforms to the description of the _form_validate.