So, I while ago I saw a theory that Andrew Ryan was the Rapture version of Comstock. That got me to wondering, is Eleanor the Rapture version of Elizabeth? Lets see how they match up.

Appearance
Eleanor: Young woman, Caucasian, dark hair
Elizabeth: Young woman, Caucasian, dark hair
Matches so far, but kinda thin, let's see what else we've got

Role in story
Eleanor: Your primary objective, need to find her in order to survive, being held captive by her mother in a literal prison, during the final level becomes a badass combat summon
Elizabeth: Your primary objective, need to find ant retrieve her to pay off a mysterious debt, being held captive by her father in a gilded cage, becomes an incredibly useful companion throughout most of the game
This matches as well, although damsel in distress is a common plot point

Relationship with protagonist
Eleanor: Was the Little Sister bonded to Delta before the fall of Rapture, kidnapped by Sophia Lamb via Hypnotize Plasmid
Elizabeth: Biological daughter of Booker DeWitt, kidnapped by Comstock via rift
Starting to get spooky similar

Relationship with antagonist
Eleanor: Being held captive by her mother in order to turn her into the 'First Utopian' to take over the surface and enforce her twisted ideals
Elizabeth: Being held captive by her father to be his heir to cleanse the surface.
My theory has legs to stand on, now for the final nail in the circumstantial coffin.

Name
Eleanor Lamb
Elizabeth Comstock/DeWitt aka 'The Lamb'

Related note, we never know Delta's real name, Johnny Topside is merely a nickname given by the press, but if his real name was Booker DeWitt I wouldn't be surprised