Akagi (An) is in the attendance list in one of the first manga chapters, but it is later revealed that Kafuka Fuura was not actually there in person. Therefore, she couldn't have been in the class as herself during the attendance check; instead she had to have been possessing one of the girls at the time. So was the listed person (Akagi An) not really Kafuka?
According to the Wikia, it's unknown (but likely true) whether Kafuka was the same person as Akagi An or not.
In the final chapter of the manga, it is revealed that Kafuka had died prior to the beginning of the series, having her organs donated to a cast of characters that indecently make up the majority of Nozomu's class. However, she was "too optimistic to die", and thus possessed one of the main female characters in every scene of the series. In the bonus chapter of the 30th volume, it was revealed, that Kafuka continues possessing girls to be able to live on with Nozomu as his wife.
However, to let Kafuka be able stay with the teacher, all the girls have to live under one roof and go through a rotation of divorces and marriages (it has to be done to let Kafuka stay teacher's wife all the time), which makes it resemble a harem.
(my applied emphasis)
we do know that Kafuka wasn't in the class during the run of the series, however, we can't conclusively tell if she is the same person as Akagi.
Personally, I believe that she is not Akagi, as Kafuka was supposedly not alive during the series, and there's not much to suggest she is a ghost.
I imagine that during the flashbacks, the students refer to the character as An because that was her actual name. Then she became possessed by Kafuka, and with time the other students started referring to her as Kafuka instead of Akagai An.