In any Other Name

I believe that Santha is saying that it is possible for a person to try and have their two personalities, but they will always return to the original personality regardless. In other words you can have two personalities but the fake one will disappear and just leave who you truly are in the end. this is seen at the very end of the story where Santha says "it all happened to a girl named Cynthia, and I was never particularly interested in her" meaning she had two personalities but her real and original one was the one she cared for and kept in the end. So you can try to have more than one personality but your original will win in the end.

I think that people can have two personalities, not identities, but personalities. this is most commonly seen in a house versus a school setting where people react to family or friends different to each other. this is seen in the story where Santha seems more at ease and outwards at home, compared to having fewer interactions at school. this is due to an environment surrounded by foreigners and a foreign type of schooling. this is seen through actions like when at home she plays with the cook's son, talks more with her mother and her sister. when she is at school she has a more introverted personae with her one friend Nalini, she keeps away to the British children due to their hostile nature towards Indians.