This Gist will guide you on how to install the No-IP DUC (Dynamic Upadate client) on a RaspberryPi and to automatically start it on boot. For this I am going to use a RaspberryPi 4B 2GB, but I have already done the same on a RaspberryPi 3B. I am going to use Raspberry Pi OS.
As a prerequisite you should register on https://no-ip.com and create the host entry that will be used later with your Pi.
First thing is to open a Terminal and create a directory to work with during the installation.
mkdir noip