Why did this NPC think Elizabeth was someone named Annabelle?

Be careful, there are deep spoilers in the spoiler sections here.

There is a part in Battleship Bay, as you're heading through the turnstile to the ticket stand, at the moment:

Right before the section where you choose whether to pull your gun on the ticketer or not

where an NPC mistakes you for someone named "Annabelle". Elizabeth also exclaims, "Well, that was odd". Is there a meaning to this? I've already finished the game, so I'm particularly wondering if:

This NPC has mistaken her for someone else in a different universe where she wasn't sold to Lutece. I'm assuming the significance is that she is mistaking her for Anna, which would still be her name if she grew up as Booker's daughter.

Why did this lady mistake her for someone named Annabelle?

Solution 1:

Needless to say – SPOILERS AHEAD!

That NPC's name is Esther Mailer. She purposely asked Elizabeth if her name was "Annabelle", so Elizabeth would correct her and confirm Elizabeth's name and identity. She was tasked to track and stop the "False Prophet", Booker DeWitt from taking Elizabeth.

From her Voxophone log, "Take Her Alive":

This is the moment we trained for. The False Shepherd is here. The day was not exact, but...the Prophet's sight proves out again. The specimen must be taken alive. If she dies, I suspect they will give us to the bird. And whatever pieces it leaves behind will bear no names...That was cigarette number six. This waiting is insufferable.

Solution 2:

She is trying to get Elizabeth to identify herself, if you pay close attention to posters and stuff you will see that Lady Comstock's first name began with an A, she is probably Annabell. Elizibeth looks like Lady Comstock, as a result of the resembalance it makee sense Annabelle would be the first name that came to her mind.