As others have already commented, what you need is a Dynamic DNS service, where you register a subdomain, and setup a small program or script on your computer that pings the DDNS server every few minutes, that way you leave that running on the background, and if the program detects that the IP with the request changes, it will update the subdomain to point to it automatically.

You could access the blog from the subdomain of the DDNS directly or if you get your own domain, you can point it to the DDNS.

If you want a recommendation, I have been using DuckDNS for years, and it has been pretty reliable.