Why Did The Mad Hatter Have A 分裂, 拆分 Personality?

Yes, there was a backstory and it was actually introduced in the film:
the whole hatter clan died which Tarrant (Hatter) was in, so he 迷失 everyone from his "family".
Another reason for his "craziness" was probably that the red 皇后乐队 had taken over wonderland and Alice was not there to help them.
And the last point is, which was not mentioned in the film, that hatter(s) back then got poisoned from the mercury which was in the glue for the hats- and this mercury made him (them) mad. That is where the term "Mad as a hatter" came from. Hope I could help.

Also, Tarrant having a 分裂, 拆分 personality was Johnny Depp`s idea, as we can see in the official interview of the movie. He made it up on the mercury problem mencionated before 由 hattersmadgirl

Mad hatter is just mad, 或者 Insane AND he drinks to much 茶 with his insane friends.