Hope following code would be helpful:
$form['names_fieldset']['remove_useful_name'][$key] = array(
'#type' => 'submit',
'#value' => t('delete' ),
'#submit' => array('remove_one_method'),
'#ajax' => array(
'callback' => 'add_more_method',
'wrapper' => 'names-fieldset-wrapper',
// add trigger
'trigger_as' => array(
'name' => 'submit_name'.$key,
), //
),
);
function remove_one_method($form, &$form_state) {
dd($_POST['_triggering_element_name']);
$submit_name= $_POST['_triggering_element_name'];
$key= str_replace ('submit_name','',$submit_name);
// You can get the $key here.
// Base this $key remove the component from the form.
......
$form_state['rebuild'] = TRUE;
}