Same with StackOverflow. Or Stack Overflow. Or SO. I don't know if it's proper to run the words together or not when written. It often appears like that around the site, but in some meta questions I see the words separated by a space.
The "official" names are Stack Exchange and Stack Overflow. If you go to the "About" page on each site, these are the only names that are used. In general usage, though, like you've pointed out yourself, the space appears to be optional. If you prefer to abbreviate, SE and SO are perfectly valid as well, similar to how English Language & Usage is often abbreviated as EL&U.
under the heading
Proper Use of the Stack Exchange Name