If this works for you in the template:
$s="[cfdb-table form="Contact form 1" show="Submitted Login,your-email,your-message" search="AndrewA"]";
echo do_shortcode($s);
then you could try:
global $current_user;
get_currentuserinfo();
$s = sprintf('[cfdb-table form="Contact form 1" show="Submitted Login,your-email,your-message" search="%s"]',$current_user->display_name);
echo do_shortcode($s);