There are a few ways to become a princess. One is to marry a prince and assume his titles and styles.
A female may be born a princess, the child of a king and queen, prince and princess.
A female may be bestowed a princess in her own right... something very rare and if done is because the woman was the wife of a prince and carried out her royal duties extremely well.
It is only a female who is born or is bestowed a princess in her own right who may correctly use the title "Princess" with her own given name. A woman who assumes her husband's titles uses the title "Princess" with her husband's given name.