wp_enqueue_script and wp_register_script in theme not working

You want to use wp_enqueue_scripts.

add_action( 'wp_enqueue_scripts', 'wpse_3810' );
function wpse_3810() {
    wp_enqueue_script( 'jquery' );
    wp_register_script( 'my_name', 'path/to/my/script/script.js'));
    wp_enqueue_script( 'my_name' );
}