Juliet asks Romeo why he is a Montague, a member of the family of her enemy.
After meeting Romeo at the ball held in her honor, Juliet has a crisis of conscience. She fell in love with him at first sight. When she first saw Romeo, it did not matter to her that she was a Capulet and he was a Montague. However, later, when she had time to think about it, she realized that his name was going to be a problem for her. Her family would never accept him.
When Juliet sees Romeo at the ball, she is smitten. The two of them share a moment full of poetry before they know each other's name. All they know is that they are attracted to each other. Romeo can bet she is a Capulet, or of the Capulet family, since it is a Capulet ball. However, Juliet would assume the same. She would not imagine a Montague would be there. Thus, when she learns his name, she is surprised.
What Juliet is saying is that she can’t believe the boy she saw at the party, with whom she fell in love, is the son of her enemy. She has been vowed to hate the Montagues, but she is suddenly in love with Romeo. What to do?
When Juliet goes home to think about it, she gets more and more upset. She looks out her window into the night, where she does not know that Romeo is lurking, and starts talking to him as though he were there (even though he is). She basically says to him, “Why do you have to be a Montague?”
Juliet does not know that Romeo is watching her, or that he is listening. He is plenty ready to give up his name for her, of course. Just like Juliet, Romeo does not care about the feud between their parents and their families. He is in love with her, and his name means nothing to him. When Juliet says, “What’s in a name?” she has a point. Romeo’s name is not a physical part of him. It may not be as easy as they think for them to be together though. Their names are still who they are. Their families will not be as understanding.
At this point in their relationship, Romeo and Juliet are deeply in love and very idealistic. The first bit of reality has hit Juliet. It is up to Romeo to convince her that he can make it work, despite the family situation. They say that girls mature faster than boys. Perhaps that is the case here. Juliet seems to be rationalizing the situation more than Romeo. Maybe he is besought by raging hormones. Either way, the two have an uphill battle ahead of them.