I really feel that Charlotte is the daughter of Ben and Annie.
I am tired of people saying that Ben is too young for this to make sense.
Ben was born in the 1960's and Charlotte was born in 1979.
My mother was born in 1961 and I was born in 1978. Believe it or not, somehow (through the magic of the island maybe), it worked.
I think Ben new the purge was coming and he told Annie to leave with their daughter and disappear and not tell Ben where they were going or what their new names would be.
Either that or there was a falling out between Ben and Annie and she left. The therapist did mention 'her' in an old episode.