When analyzing a character's personality, we are analyzing characterization. Characterization is how the author portrays the character as a person. There can be both direct and indirect characterization. Direct characterization is when an author comes right out and says what the character is like in the narrative. Indirect characterization is when the author takes a more subtle approach, showing us what the character is like through the story by allowing us to see how the character acts, thinks, and feels. We can even observe characterization through how other characters respond to the character in question, what they think of that character. Since Romeo and Juliet is a play, all of Shakespeare's characterization of Juliet is indirect and must be analyzed through the things she says and does. A few things we know about her personality through indirect characterization is that she is a kind, respectful person, but has a strong will and is even a bit stubborn.
We especially see Juliet acting respectfully towards her mother in the third scene when we first meet Juliet. Lady Capulet is trying to convince Juliet to think of marrying Paris. Adhering to her role as a respectful and obedient daughter, Juliet promises her mother that she will consider Paris, saying, "I'll look to like, if looking liking move" (I.iii.101). However, even in this very first scene, Juliet demonstrates just how much she values her own opinion, proving herself to be strong-willed and stubborn. For example, we see Juliet expressing her own opinion when Lady Capulet asks her what she thinks of the idea of getting married, and Juliet replies, "It is an honour that I dream not of" (70).
We especially see Juliet's kind nature with respect to how she treats Nurse. When her nurse returns to the Capulet house with a message for Juliet from Romeo about arranging their marriage, Juliet is desperate to learn the message, but continues to treat her nurse with kindness, calling her pet names, like "honey nurse," "sweet nurse," and "good nurse" (II.v.18, 21, 29). Even saying, when the nurse complains of her aching bones, "I'faith, I am sorry that thou art not well" (54).