I am not sure if your are using a static or dynamic ip address but you can use a dynamic dns client to automatically update your url to your ip address automatically all the time.
If you have registered your own domain name than I would recommend you to stop by zoneedit.com and register with them. They will provide you with free domain name servers for up to five domain names I believe. After the five domain names than they start charging you. But it's a good start and I have never had any problems with them and they have excellent support.
Using zoneedit.com's name servers and a dynamic dns client such as ddclient you will be completely good to go for up to five domain names.
If you are looking for free domain names to use and a dynamic dns client to use than I would recommend you to stop by at dyndns.org, register with them and than your can register as many free domain names with them as you wish. You can also grab a dynamic dns client from there as there are many to choose from for free.
As for setting up multiple web sites on your box as I have done so myself, which are called virtual hosts, just check out and read through redhat's documentation on Apache HTTP server configuration located at the following url:
Just read through it step by step and you should be good to go.
I hope this helps, and good luck.