Becoming a woman
Becoming a woman is a possible theme because through out the diary we see Anne mature. One example of this is Anne's love life, Hello Silberberg is someone who Anne has a relationship with before she goes into hiding. Right about when she goes into hiding is the peak of her womanhood.
Coming of age
Coming of age is also a possible theme because in the diary Anne isn't the only person who matures, some of the male characters do too. One example of this is Anne's Father, We also see him mature at about the time the go into hiding as he begins to take more risk for his family and protects them more.