What does Juliet mean by "what's in a name?" How do people relate to their own name? How do other's relate to a person's name?
"What's in a name?" is a question Juliet asks of herself out of frustration for Romeo's (last) name. Because Romeo is a Montague, by default, he is a mortal enemy of Juliet, who is a Capulet, and therefore, he is not someone she will be allowed to date. Of course, this creates many problems for the "star-crossed lovers" which are ultimately overcome by their untimely deaths. According to Juliet, a name is just that: a name and nothing else. No further significance should be attached to it.
Names relate us to our family members, living and dead, near and far. They signify cultural heritage, religious beliefs, and sometimes origination of a family. I relate to my own name in these ways. Others probably relate to my name based on understanding (or lack thereof) of its Italian meaning. It connects me to other family members who have gone before me, and often raises awareness of who I am among elderly members of my community.