The chief concern that Juliet displays in this famous balcony scene involves her name and the way in which names hold such dominion over her life and that of her beloved. This is because, as both we and she knows, it is the name that Romeo bears and that she bears that are keeping them apart, as the feud that rages between their two rival houses means that any hope of a marriage between them that is recognised and accepted by their parents is an impossibility. Consider what Juliet says in this scene:
What's in a name? That which we call a rose
By any other word would smell as sweet.
So Romeo would, were he not Romeo called,
Retain that dear perfection which he owes
Without that title.
Juliet shows her ironic awareness of the fact that Romeo, were his name not Romeo Montague, would be an excellent suitor and husbnad for her. It is only his name that makes their happy union and marriage together impossible. Even a rose if it were called something else would "smell as sweet," and so Romeo, if he had a different name, would likewise be just as handsome and pleasing.