Santha resolved the conflict that she had with the headmistress because she never thinks of herself as being "Cynthia". She believed that having two names simply mean that the person will have two personalities.
The story was about discrimination of some Indian children. Santha and Premila were sent to English schools because their father was working in a village that was close to the school. Their father was in the army.
When they got to the school, the headmistress informed them that she couldn't pronounce their names. Therefore, she changed Santha's name to Cynthia while Premila's name was changed to Pamela. They were discriminated against while in the school.
In conclusion, the main message about the story is that there should be fairness in the world and that people should love one another.