Web search "dns hosting". There are dynamic DNS services that can resolve a fixed name to a dynamic IP, as long as you either have a compatible router that supports updating that DNS service, or run an app on a computer that periodically tickles their server to grab your connecting IP. I have used noip.com. They do charge a nominal fee if you want to have them resolve your own domain instead of one of their free subdomains.
Note that once you have arranged dynamic DNS, you would need to give your domain registrar the nameservers of the service, as authoritative nameservers for your domain.
There's also something called Hamachi (related to Logmein) where you would have a static IP on the Hamachi VPN. But if you want to have more than 4 others connect to you, there would be a fee instead of free. People would need at least a free version of Hamachi to connect to you.