After downloading and installing noip2 you need to take a few more steps.
The noip2 binary is installed in the correct directory (/usr/local/bin) but the noip2.sh file is not, it remains in the installation directory.
1) move noip2.sh to /etc/init.d/
2) rename noip2.sh to noip2
3) add the following lines near the top of noip:
### BEGIN INIT INFO
# Provides: noip2
# Required-Start: $remote_fs $syslog
# Required-Stop: $remote_fs $syslog
# Default-Start: 2 3 4 5
# Default-Stop: 0 1 6
# Short-Description: Start noip at boot time
# Description: Enable noip service provided by daemon.
### END INIT INFO
4) execute sudo update-rc.d noip2 defaults
5) reboot and execute ps ax | grep noip2 to confirm that noip2 has started automatically.
The noip service will be started in the appropriate run levels. You can also use
service noip2 start/stop
to manually control the noip service