I expect we’d adapt pretty quickly to the idea that there exists a new possible degree of relationship between people, namely the relationship between two people who used to be the same person.
If you count a fertilized egg as a person, then two identical twins did use to be the same person. :-)
If you count a fertilized egg as a person, then two identical twins did use to be the same person. :-)
And chimeras used to be two different people.