$(document).ready(function() {
    var $select = $('#select');
    var $custom = $('#custom');
    var customValue = 'Другое';
    
    $('#form').on('submit', function() {
        var $element = $select;
        if ($select.val() == customValue) {
            $element = $custom;
        }
        $element.attr('name', 'value');
    });
    
    $select.on('change', function() {
        $custom.toggle($(this).val() == customValue);
    });
});