Você deve adicionar seu script aos padrões de runlevel:
sudo touch /etc/init.d/noip2
sudo chmod 755 /etc/init.d/noip2
sudo update-rc.d noip2 defaults
Em seguida, adicione isso em /etc/init.d/noip2
#######################################################
#! /bin/sh
# . /etc/rc.d/init.d/functions # uncomment/modify for your killproc
case "$1" in
start)
echo "Starting noip2."
/usr/local/bin/noip2
;;
stop)
echo -n "Shutting down noip2."
killproc -TERM /usr/local/bin/noip2
;;
*)
echo "Usage: $0 {start|stop}"
exit 1
esac
exit 0
#######################################################
Em seguida, reinicie e seu script estará em execução.