In the Silver Age of Comics, Hawkgirl's real name was Shayera Hol. The name "Shayera Hol" isn't exclusive to the DCAU. Shiera Hall is the real name of the Golden Age Hawkgirl and the alias of the Silver Age Hawkgirl, who is the one described in the biography.
I know. I just thought I'd inform you because I assumed your only experience with the DC Universe was the from DCAU since her name in that was Shayera Hol. It's a common mistake. Just look it up next time instead of changing it.
Well, it wasn't a mistake. My assumption was that Shayera Hol instead of Shiera Hall should be listed under the Real Name section. If Clark Kent istead of Kal-El is listed as Superman's real name, however, then I have no problem. I still think Shayera Hol should be mentioned as the Thanagarian name of Hawkgirl in the biography though, as Kal-El is mentioned as Superman's Kryptonian name in his biography.
It was a mistake. The game lists her name as Shiera Hall. No more information is needed. Besides Shiera Hall and Shayera Hol are just alternate spellings while Kal-El and Clark Kent are the phonetically different. There's no need for redundance.
If her real name, not alias, is Shiera Hall, then she's a human. As such, her entire bio should be revised to match that of the Golden Age Hawkgirl because the bio on the Hawkgirl page gives the real name and reincarnation aspect of the Golden Age Hawkgirl but the origin of the Silver Age Hawkgirl. The first Hawkgirl from the Golden Age was a reincarnated Egyptian princess named Shiera Hall. The second Hawkgirl from the Silver Age was a Thanagarian with no relation to a reincarnation cycle, the real name of Shayera Hol, and the human alias of Shiera Hall. Hawk-Continuity is quite confusing when you have two characters that are referred to by the same name. By the way, the Injustice: Gods Among Us website lists Hawkgirl as Shayera Hol.
Follow the link on her talk page. Her official Injustice bio lists her as Shiera Hall, a human. Therefore there is no need for her Thanagarian name. The Injustice: Gods Among us bio you're referring to links you to her official DC Comics bio, which is different from the video game. As I said before, look it up next time.