Drop-Down Menu of Current Child Pages

Question

This can be approached by using wp_dropdown_pages() with the child_of parameter.

global $post;
$args = array(
    'child_of'         => $post->ID
);
wp_dropdown_pages( $args );

The variable name will be $_GET['post_id'] or $_POST['post_id'], depending on your form settings, you can change the name by altering the name parameter. The value of the variable is the ID of the chosen page. Use get_the_title() to get it from the id in your $_GET/$_POST variable.