Yes, You can setup another domain name on your existing hosting plan.

Let me explain how that works. :)

Assume that you purchased a hosting plan for domain xyz.com. Now you have another domain abc.com for which you want to have website but don't want to purchase another hosting plan, to minimize costs.

You can setup addional domain abc.com in the xyz.com control panel under cpanel "Addon domains" option.

Internally addon domain abc.com points to a subdirectory in the main domain xyz.com/abc. These addon domains operate like regular domains and you can access them from a browser as http://www.abc.com but all the files for this website will be stored and retreived from xyz.com/abc directory.

This way you can actually have several different web sites hosted in a single hosting account.

Please see the following visual tutorial for creating addon domains on your hosting plan. http://www.fastwebhost.com/tutorials/cpanel_xskin2_addon.htm 

Note: You will not get a separate control panel (cpanel ) for the addon domain.