Are you referencing the post-credits ending when Booker enters the bedroom beside his office? Because technically, we have no idea if there is a baby or not. The insinuation is that there is a child there, but you never see it (you hear noises and see the crib but that itself is insufficient). Even if there is a child, the calendar on Booker's desk shows the date Oct. 8, 1893, which is the same date when Robert Lutece arrives to take the child from Booker in the original plot (meaning Booker had to have been baptized prior to Oct. 8, 1893).
Seeing Booker at the end of the game is not an indication that we are continuing the same timeline, but, more likely, we are getting a glimpse of an episode of the post-baptism Booker either within the original timeline or one of the infinite variations of Booker that may exist within the multiverse. There may very well be universes in which Booker doesn't turn over his daughter to Comstock, creating a whole different subset of existences and possible storylines. But regardless, when you think of time as a linear progression, if a choice is altered in the founding reality that renders the existence of the consequential multiverse impossible, it doesn't exist. But getting a glimpse at the "theoretical" instances within an "impossible scenario" isn't an innate contradiction of the rules established by Infinite's universe.
Also, Elizabeth is the name Comstock gave his child (presumably) - Anna is the name Booker gave his.
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