Are you trying to get a domain name i.e. you want to go to a browser and type in something like codenamevirus.com and it resolve to one of your sites? If so you will need to register the domain name to your static IP.

But that doesn't really matter since you can connect to your modem given its static IP. Make sure your router is not blocking all incoming connections and forward a port to the IIS. That way all connections that go into your modem requesting a certain port gets forwarded to the IIS since you are behind a NAT. I do suggest though that you read through some IIS manuals so you have a good idea on what is going on and can properly configure it.