In this speech, Juliet acknowledges the difficulty in being with a Montague, as she is a Capulet. However, she argues that these names are just words. They are not intrinsic to the person. Romeo would be the same person, whether he was a Montague or not (just as a rose would have the same smell even if it was not called a rose). Therefore, she asks him to renounce his name, and no longer be a Montague. And if he feels he cannot do this, she will stop being a Capulet.