A simple service for only one purpose - running your own dynamic DNS.
You need a (Linux) server in the Internet and a domain with access to the nameserver settings. Create a NS record for a sub-domain of your domain (e.g. home.example.com) which points to your server. On your server install and run the mpddns server. Run periodically the mpddns client from within your home network to update the sub-domain with the IP of your Internet access.
For the server, see the example config file in directory etc/. If the server was started without any parameters, it looks at /etc/mpddns/mpddns.conf for its config file. Use the command-line option -c to change this behavior. The server will start into background (as daemon), log messages will go to the system log.
The client has no config file, check the command-line help for the required arguments