You do not have to add the usual URL suffixes like .com or .net. The number of sites that Cortana is working with at the moment is limited. So far, sites that Cortana will load up include Google, Facebook, Yahoo, CNN, Pizza Hut and Wikipedia
Considering that this feature requires Cortana to work closely with the native browser on the phone, it seems that this new capability won't be made available immediately to the Cortana for Android app, or the upcoming Cortana for iOS app. The latter is currently being beta tested.
Let's say you want to open the CNN website on your Windows 10 Mobile phone. Opening Cortana and merely saying CNN will result in a message that says "I'm pulling up CNN," followed by the opening of the CNN homepage on your screen. There is no word on when Microsoft will expand this capability, and how many sites will be eventually be capable of getting opened like this. Previously, Cortana could launch a website by vocal request only if that site was pinned to a phone's start screen.