I don't think TNA has a true face, and that's part of the problem. One of their main problems is that they don't have a true direction; their story lines are all over the place, featuring different guys at different times, without really picking someone as their main guy, whether he be a face or a heel. TNA lacks the one go to guy, which does not necessarily have to be a bad thing, but in their case, I think it is.
I guess it all depends upon how you define the face of the company. I see the face of the company being the guy(s) you build the company around and move forward with over an extended period of time. John Cena and Randy Orton are the faces of WWE. They are always prominent in the story lines, whether the title is involved or not, although it usually is.
Sting cannot be the face of the company at his age, as I don't think the "face of the company" changes every couple of months. He cannot and will not be around much longer. I could make the same point about Kurt Angle, who may be the current Heavyweight Champion, but his health and age, and his lack of regular appearances on TV for extended periods of time, prevent him from being the face of the company. Jeff Hardy is hardly the face for obvious reasons, and Anderson isn't because he's not good enough to be.
AJ Styles should be the face of the company, but he isn't and likely never will be, especially as long as Bischoff and Hogan are around. Rather than making him the face of the company, they will continue to underutilize him in meaningless feuds with the Dudleys and Tommy Dreamer. And TNA will continue with no true face of the company, no one to progress forward with as they strive toward the 1.5 barrier.