https://www.duckdns.org/ - I've used this.
https://dns.he.net/ - Hurricane Electric free DNS has a DDNS service now (BYO domain)
A thread on Slashdot, April 2014, after DynDNS completely ended the free level of service - http://tech.slashdot.org/story/14/04/07/1450222/dyncom-ends-free-dynamic-dns
DDNS update clients:
https://updater.marc-hoersken.de/ - used this ages ago - in 2020 does not allow custom ddns providers, nor has he.net on it's list.
Gone (non free): Dyndns.org
tags: hostname, ip, dynamic, dhcp, ddns