Alternative they could name it after political leader (Conderation of Jefferson) or a concept (Liberia, Freedonia, Libertiria, Big Ballia).
Jefferson would be the most likely, I suspect. The South hasn't ever exactly a freedom-friendly region[1], sadly, so unless there is a truly radical change in society and culture, I don't think any of the other three serious names would fit, unless you're be going for an Orwellian theme or something along those lines[3].
[1] Yes, that means real freedom, btw(such as no bans on interracial and/or LGBT sex/cohabitation/marriage, cannabis, etc.), and not the false B.S. typically peddled by certain types of malcontents based on no taxes, unregulated weapons ownership, unregulated business conduct, etc.
[2] And I mean truly radical, not just a few replacements and some small twists, like in DoD or Turtledove's "Confederacy" series, but something full-blown like Jello's "Red Dawn" TL, something that would even impress the Founders of the U.S. or France's Revolutionaries in its scope.
[3]But given the history of the South, that may not be so far-fetched.