Yes, you would need a valid domain name as you noted, in your example your domain would be wisconsin-jim-makes-great-homebrew-beer.com, which you'd purchase from a name registrar.
There are several moving parts to this though; you'd either need a static IP address from your ISP, or, assuming they don't hand out static to residential customers (most don't), you'd need to use a registrar that supports dynamic DNS updates. I've never used dynamic DNS since I've had a home static for many years so I really can't help with the dynamic update aspect. You could take a look at a registrar that has free dynamic DNS service, and a Windows dynamic DNS update client at:
Dynu they seem to have good documentation and you can purchase your domain name directly through them.
If you have a static IP through your ISP then it's a much easier task; you purchase the domain name via the registrar, log in to the admin panel and then add whatever hostname to the DNS section as an 'A' record, in your example that's the "www" part of wisconsin-jim-makes-great-homebrew-beer.com, then you'd enter your static IP to that 'A' record.
Unfortunately, Letsencrypt does not yet issue certs on IP addresses but they're planning to do that in the near future. They have a blog post on how that will work here:
We've Issued Our First IP Address Certificate This might be a really good option but I'm not sure if
@ProScan would need to add new code to support it. The IP based cert will only be valid for 6 days so renewals would get tiresome doing them manually. But, this option would eliminate needing a domain name registration and all the extra complexity that goes with it. The only issue is if you have a residential broadband dynamic DHCP IP you'd have to do a full certificate issuance every time the IP changes, it wouldn't be just a renewal on an existing certificate.