As with many young girls of her age, Anne looks upon her diary as a close friend, someone in whom she can confide her innermost thoughts, fears, and desires. As the diary is more of a person than a little book, Anne gives it a name—Kitty.
There's no particular reason why Anne gives her diary that specific name; it just happens to be a common girl's name which fits the identity of a trusted friend. However, Anne did think carefully about what name she would give to her diary. At first, she thought about calling it Jettje or Emmy, but she finally settled on Kitty. She settled upon a name and an identity to whom she was comfortable addressing her deepest thoughts. From then on, all her diary entries would begin with "Dear Kitty . . ."