$(document).ready(function() {
    var $select = $('#select');
    var $custom = $('#custom');
    var $customValue = 'Другое';

    $select.on('change', function() {
     $name =  $(this).val();
       if  ($(this).val() == $customValue) {
         $('#custom').show();
        }
else {
$('#custom').hide();
}
    });

 $('#form').on('submit', function() {
         if ( ($select.val() == $customValue) && ($custom.val() != '') ) {
            $select.val() = $custom.val();
        }
      else{
      $select.val() = $name;
      } 
    });
});