A Dual Identity For Your Domain Isn't Good for Search Engines
Bottomline: Be consistent in the website address you use everywhere online. Dual Identity = Bad for SEO.
In Google’s robotic eyes, YourDomain.com and www.YourDomain.com are very different websites. This means that if some of your links are pointing to YourDomain.com and some are pointing to www.YourDomain.com, you’re not getting the full credit for your links and your search rankings will not be as high as they could be.
If you’re leaving comments, getting links or do anything on the web, be sure to pay attention to what your real website address is. If when you put in http://www.yourdomain.com, it redirects you to http://yourdomain.com, that is what you want to use in all your links and comments.
If you’ve already got all the links and comments pointing to www.yourdomain.com and your website address is http://yourdomain.com, you can change your settings by going to Settings > General from the left side menu and making the change over there. How can you find out? Use a tool like MajesticSEO.com.