I'm pretty sure that Sinclair was only allowed to use the "Fox" names for a limited time, and it really makes no sense for two companies to both call themselves the same thing. Note that there is now a "Fox Sports Go" app for Sinclair and a "Fox Sports" app for Fox and its national sports channels, which is confusing. I'm sure Fox still gets mail complaining about stuff Sinclair has done.
As to Ohio, "Cincinnati" is just an internal label Fox used for its Cincinnati coverage. It never has appeared on camera, just in channel guide listings. With the Indians now on a different channel and the Cavs now on in Cincinnati (they did not used to be) the only major differences between the feeds is that the Cincinnati feed includes the Reds (and BJs and Cavs) and the "main" feed includes Columbus soccer team, BJs, and Cavs.
As to college conferences, the only two that have a proper name are Conference USA and the American Athletic Conference, which are conferences and are in the USA/America. The Big 10 has 14 members; the Big 12 has only 10, only 2 of which are actually big; the Pac 12, while having 12 members, includes such Pacific states as Utah, Arizona, and Colorado; the SEC which includes such southeastern states as Texas and Missouri; the ACC has such Atlantic coastal cities as South Bend, Syracuse, Atlanta, and Louisville; the Mid-American has that quintessential Midwestern city of Buffalo, NY, while the Sun Belt includes the ski resort town of Boone, NC; while the Mountain West has three members in California and one in Hawaii.
