Hi Christopher,
The set-up you have at the moment is actually fine for SEO - http://www.fdmgroup.com/ resolves the website. http://fdmgroup.com/ employs a 301 redirect to take users and search engines to http://www.fdmgroup.com/: http://i.imgur.com/et4AKYV.png
This is correct, http://fdmgroup.com/ would be seen as a separate "version" of the home page if it was allowed to load without sending everyone on to the "www" version via the 301 redirect. Furthermore, every page within the http://fdmgroup.com/ "version" of the website would be duplicated from the "www" version of each page.
If you want to change to use http://fdmgroup.com/ instead, using that both on advertising and having that be the version of the website that resolves for both users and search engines, you will need to reverse that 301 redirect. This will mean that when people try to visit http://**www.**fdmgroup.com/, they are redirected to http://fdmgroup.com/. This is a simple process.
However, it is inadvisable to go through redirection like this unless you really, really have to. When you redirect a URL with a 301 redirect, a large portion of the URL's authority is passed on to the new URL. Not all of the authority is passed though. As a result, your rankings and traffic can take a little hit for a short while. This is not usually a big problem, and usually resolves itself quickly but it is best avoided unless the redirection really has to take place.
I am tempted to say that "it looks cleaner" is not the best reason to go through this change when your current set-up is totally fine and correct for SEO purposes.
That said, you absolutely could reference fdmgroup.com in offline advertising for stylistic purposes. When people type that URL in, they'll be redirected to the www version just as they are now. This is pretty common because of the stylistic benefits of not including www in TV / print advertising.