I believe that the term "Open Source" is the one most accessible to a general audience.
People like Richard Stallman make good points about why the term "free software" might be better, but unfortunately the semantics of the term did not enter the general language use. When you use the term "free software", most people still think of free as in beer, not free as in freedom. So when we call the site "Free Software Stackexchange" we will receive lots of questions about software which is proprietary but free to download, which is not what this website is about.
Using "Free and Open Source Stackexchange" (is there a length limit for site names?) doesn't solve the problem either. Because "Free" does mean "Free as in beer" for most people, it will give the misconception that it implies that open source must also be free as in beer to be on-topic for this site and that open source software must not cost anything, which is very wrong and would alienate many of the most interesting topics from this site.
The acronym "FLOSS" is even worse, because even fewer people know what it actually means. Also, when you don't know that the context is software, a website "FLOSS stackexchange" would sound more like a website about dental hygiene than one about free and libre (who uses the term "libre" anyway?) open source software.
For that reasons I believe that "Open Source Stackexchange" is still the least ambiguous name we can use.
However, I think that the term free software should appear in the site description, preferably in a way that it makes clear we are talking about free as in freedom.