I'd have her named Daisy or Lily. So, just what became of her once all of history was rewritten by Jake's wish?

The new Rose seemed to have no knowledge that even had a sister; and an identical twin at that.

She could not have been erased from existence! She and Rose were still born on the same day or night, with her dragon-shaped birthmark being the only way to tell them apart.

And what would Jake have thought of her anyway?