Roland first pulled susannah through that door from New York into his world. She had the personality of Odetta and Detta I believe. Am I right?
Yes. Or Odetta and Detta are two women in one body...depending on how you'd like to view it... Susannah being a merger of the two.

That being said I heard a theory that Susannah was just another third personality. It is kind of interesting that as Susannah she can still draw on, or listen to Detta when she needs to. In fact sometimes she even comes forward unbidden although she seems a slightly less vicious anarchic version than the one who manifested originally.