Not an expert as such, but I see A is a clear winner here.
To many citizens of Napoleonic-era France, before Haiti was Haiti, it was Dominique, a small province of France that produced sugar cane, rum, and tobacco.
(A) before Haiti was Haiti, it was Dominique
(B) Haiti was Dominique, before there was a Haiti
(C) before there was Haiti, it was Dominique
(D) Haiti was what was known as Dominique
(E) Haiti was what had been referred to as Dominique
Solution:-
B) the sentence in the latter half must be describing Dominique, here it does Haiti - clearly illogical
C) would be correct to say "To many citizens of Napoleonic-era France, before there ever was Haiti, there was Dominique, a small..." ie there and it are at a mismatch
D & E) meaning not maintained. They both say that Haiti was referred to as Dominique, but it should have been clear that it was called Dominique before it was called Haiti
Coming to the right answer:-
(A) before Haiti was Haiti, it was Dominique
While this choice may seem odd, it can be seen as :-
To many citizens of Napoleonic-era France, before Haiti was (called) Haiti, it was (called) Dominique, a small province of France that produced sugar cane, rum, and tobacco.