I think the short answer is No, but I also think this is not the best question.

The better question is: are there any contexts in which it's useful to think of the person in Mary's body as the same "person" as was previously in that body?

And to that, I still think the answer is No.

And that's because the only reason why it's useful to "recognize" or "identify" people over time is so that we can form predictions about how they will behave in the future, based on how they've behaved in the past - i.e. based on their "reputation".

And in the case of Mary's body, which now has no trace of it's former brain, there is essentially no continuity with the "person" we used to refer to as "Mary", and therefore, no reason to expect her to behave at all in accordance with the reputation Mary used to have.

By a similar token, Terri and Carrie have also undergone a sharp "break" under which it may be hard to establish continuity with any of their prior actions, or, therefore, to predict their future actions.

If, for example, Terri had committed a crime, should we put Terri's body (with only half of her brain) in jail? And what about Mary's body, which now has the other half of Terri's brain?

At some level, the answer depends on which half of Terri's brain (if either) is likely to commit the same crime in the future. If it was a heinous crime, like a murder, then we should probably put both Terri's and Mary's bodies in jail, because both are too big of a threat to everyone else. But if it was not so dangerous, then maybe you can just wait to see if either body commits another crime.

The only logical reason why we should ever punish or jail (i.e. quarantine) someone is if we think it will prevent future crimes. We've developed myths about people "deserving" punishment, but that is a totally incoherent worldview. Because "deserving" relies on "free will", which is also incoherent. But "prediction", based on past behavior - now that is perfectly coherent and sensible and useful.

The only useful way to think of "identity" or "reputation" is with respect to what behavior we can "anticipate" or "predict" from someone.

People agonize about what their "identity" is. But really, a person's identity is all about what other people expect, anticipate, and predict from us, and what we expect, anticipate, and predict from ourselves.

That's the only coherent way to think about identity. Everything else is just myth making and nonsense.