One per season.
Ivan Maisel brought it up in his column at ESPN.com and yes the debate continues to be dumber than a box of rocks if for no other reason than the fact UNC was here first:
So when you think of Carolina, do you think of the Tar Heels or the Gamecocks? The debate over the identity of the real Carolina continues this fall on the cover of the football team's media guides, which are almost identical in design.
North Carolina grabbed "Carolina Football." South Carolina sticks to "Carolina Gamecocks," the thought being that the mascot prevents any confusion. But you have to have some sympathy for South Carolina. The school doesn't own Carolina. And it can't even claim its own initials. Southern California got there first.
Perhaps winning a few Southeastern Conference championships would get the Gamecocks over the identity hump. Or even one. Or even an SEC East title. Head coach Steve Spurrier said when he came to Columbia that he wanted the challenge of doing what had never been done. Winning games, and winning ownership of "Carolina" and "USC" -- it's all the same.
Granted this has been going on for years, but Steve Spurrier has a burr up his rear end about this and thinks that somehow he can make people think Gamecocks with you say Carolina. Not so much. Even if Spurrier finds a way within NCAA regulations to win a few SEC titles you still do not win the battle for "Carolina" The reason being is, unlike SCAR, the University of North Carolina enjoys a wide ranging identity across multiple sports in the form of national championships. Compare that to the one NCAA title SCAR owns in women's outdoor track from 2002 and you begin to realize is across the board there is only one true Carolina and the one in Columbia ain't it.