Board Thread:Wiki-Related Discussion/@comment-26261153-20150720230151/@comment-2153169-20150728005447

Belle's amnesia is her counterpart. Remember when she crossed the town line? She forgot everything from her EF life, and what do we have at the end? Amnesia Belle. Just like David when he was "John Doe", the amnesia is a part of their cursed persona. Then, Regina did to Belle what she did to David; she "activated" the false memories part of the Dark Curse, giving us Lacey. So yeah, Amnesia Belle was a part of her cursed persona. The first "form" of the DC, which was the same thing for all inhabitants. The DC erased all their EF memories, and gave them new memories for SB. Belle was just blocked as the first form during a long time. EF Belle -> Amenesia Belle thanks to DC who evolved to Lacey thanks to Regina.

Exact same thing with David/John Doe; the only difference? Regina activated David's false memories at the beginning of S1 so people have zero problem with him.

And, as I already said, she has a last name. Her father is Moe French. Even if Belle is not cursed currently, she clearly assumes a new SB identity, Belle French, which is the same thing for Regina. Even if their personalities are not completely cursed like others peoples, the DC gives them a new and clear identity.