Dynamic DNS
Dynamic DNS for self-hosted sites where the IP address changes.
https://www.dynu.com/ - free and lets you use own domain. Seems to be one of the easiest to set up.
https://www.dynu.com/DynamicDNS/IPUpdateClient/Linux
Seems like we can use a full domain name with this.
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freedns.afraid.org - use a subdomain on one of their domains, or point your own domain to your server. Has Clients for Mac, Linux, and windows. Many other services too, free.
duckDNS - not as many services but does dynamic DNS and is free.
http://freeddns.noip.com/
Another possibility
With URL forwarding at the DNS provider, we could point any domain to the subdomain of the dynamic DNS provider and host anything on a cheap machine. People could even donate a small cheap pc connected to their home modem, which depending on the bandwidth available, would likely provide a far better service than a cheap VPS.
found this too: