The best way to do this is to subscribe to either Google Apps for Business or an Office 360 business account. With these paid services, you can configure them to use your domain name and they will provide polished Email, Calendar, Contacts, and cloud storage services.
Both of these serivices offer calendar invites and they will come from your domain because their email and contacts are well integrated into all of the services.
Both services are great so you should decide if you interact with more people that use Microsoft Exchange (Outlook) for email or those that use Gmail or Google Apps. Go with the service that more of your contacts use.
The beauty of either service is that they both offer great web interfaces for laptop and desktop computers and also work seamlessly with iOS devices like iPhone.