Save the username of the user that updated the form in a field.

add_filter('frm_update_entry_meta', 'update_field_value');
function update_field_value($new_values) {
   if($new_values['field_id'] == 11389) { //11389 is the ID of the hidden field in the form - note that this field must have a value in it on form submit or this code will not work
		$user= wp_get_current_user();
	   $username=$user->user_login;
	$new_values['meta_value'] = $username;
   }
return $new_values;
}