All depends on has your site side a public IP-address at all? If
the provider providing your connection by dynamic but real public
IP, you may use free service, for example: https://freedns.afraid.org/
It provides free dynamic DNS support, when you able to choose a subomain name for your own connection. The router will register dynamic address every time it's reconnecting. So you may access your site by DNS name most of time. The limitation: You had to enter your account at freedns.afraid.org at least once a year to not lock DNS operation.
But... A fewer and fewer providers are able to provide whole IP address to single client. Most of connections, at least, private persons, are behind of a CNAT and are sharing IPs.