Why are these Shakespeare lines so significant?

I'm not sure what you are asking...but I guess they are important because it is Juliet asking Romeo to refuse his name, disown his name...because his family and hers are enemies. She is also saying that if he wont, she would. It shows how much Juliet loves Romeo, and how far she is willing to go, to disown the name of Capulet...to be with Romeo.