Even if you have a dynamic IP address from your ISP, this can still be done - rather inexpensively. Some [http://en.wikipedia.org/wiki/Dynamic_DNS dynamic DNS] services, like DynDNS, allow for you to create a domain and use something called a [http://en.wikipedia.org/wiki/Wildcard_DNS_record wildcard DNS record]. This acts much like the subdomain created above, but you can literally use anything you want so long as the server is set to answer to the request. Below, we'll outline the basic steps needed to accomplish this.
Some routers (Netgear, Linksys, etc.) allow you to set up credentials for your dynamic DNS service account so that it'll update the dynamic DNS service for you. If you don't have that ability, you may have to run a client-side application on a computer inside your network which will send out regular updates to do the same thing. Figure out if you will be updating the dynamic DNS service via the router or a client-side app. Once you've confirmed you can utilize this technology, in one form or another, proceed with the rest of these basic steps.
# Obtain a ''paid'' DynDNS account.