OS X Server 3.0 - DNS & Server Names
Domain Name System, or DNS, 


  translates easily memorized domain names to the numerical IP addresses


For what you are asking all that is necesary is two DNS records specifying the same IP address. You could make your Mac Mini Mavericks server aware of the multiple domain names, using an alias, but it is not an absolute necessity to have the functionality you seek. 

The questions that remain are:


Whom or what is handling your domain names, and translating your public address to the IP of your server? Your ISP? 
Did you reserve and purchase your desired domain names?




Possibly of some use to you is this tutorial, How to Configure OS X Mavericks Server App 3.X Basic DNS and Server Settings

You'll find a more advanced an in-depth explanation of DNS here