What is dynamic DNS ?
https://www.dynu.com/en-US/DynamicDNS

For a long time, DynDNS is the choice from many users. DynDNS is pretty good at what it does and has almost every feature you’ll ever need like awesome premium domain names, multiple hostnames, rapid propagation, etc., as a home user. However, as good as it is if you want to use DynDNS you need to pay $55 per year. Depending on where you live and what you use dynamic DNS for, $55 pricey. Moreover, DynDNS is constantly increasing the prices year over year.

So, here are some of the DynDNS alternatives you can try for free.