First you need to register your domain from a registrar. Patheticcockroach.com is registered by
1steuro.
Godaddy is a more famous registrar, but you need to give away your credit card number so I didn't test them. There is also
Dolster. You shouldn't pay more than 15$/year for a .com domain name.
Then you should set up a redirection to your IP. Note that only some registrars offer this redirection. In the case of 1steuro, I think you need to pay like 1 more euro per year for the forwarding. The only problem with the forwarding is that your visitors will still see your IP at some point, there is a way to avoid this but this implies setting up a DNS server which I don't know how to do.
If you don't want to pay for a domain name, you can use
no-ip.com to set up a redirection like this one :
http://mpam.myftp.biz:8081/phpbttracker/