You can do what you want with a ‘dynamic DNS’ service. That gives you a host name which can refer to your home’s dynamic IP address. You run a piece of software on your PC or router that signs in to the dynamic DNS service and keeps it updated with your current IP address. Totally doable.
You may have a great router, especially if flashed with DD-WRT. If it is, then you can set it up to automatically update your dynamic DNS account, and not rely on your PC to do it. That’s how mine is set up.
<a href=”http://www.dyndns.com/”>Here’s the dynamic DNS service I use (I use a free account).</a>
<a href=”http://www.dd-wrt.com/site/index”>And, here’s the link to DD-WRT (if you are interested, as it is optional).</a> You’ll have to see if your particular model of WRT54G is supported or not.