The main theme of "By Any Other Name," by Santha Rama Rau is that personal and cultural identities are important.
In this Anglo-Indian day school, both girls were given an Anglo name because their names were said to be, "hard to pronounce." Even if the narrator, Santha, was the same person, she felt detached to herself as "Cynthia," in school. It was as if it was another person because she had to be someone else, once she entered campus. She and her sister were brought up in a different culture and they felt that in their school as they were often segregated and singled-out because of their race. In the end, Premila had enough of the discrimination and she and her mother decided that it was not a school to go back to. Even when they thought that Santha did not understand what was happening, it was revealed that she did.
This shows that personal and cultural identities are important because no matter what happened in school they maintained to be themselves as they were brought up to be and rejected the person they "should" be in school.