“O Romeo, Romeo! wherefore art thou Romeo?
Deny thy father and refuse thy name;
Or, if thou wilt not, be but sworn my love,
And I’ll no longer be a Capulet.”

By denying his father, Romeo would be rejecting the name of Montague–”‘Tis but thy name that is my enemy.” Juliet’s alternative, if Romeo will swear he loves her truly, is that she’ll deny her own name–Capulet. This leads her on to contemplate “What’s in a name?” which is an interesting philosophical point. If what we now call a rose were to be called “cabbage” (say) it would still smell sweetly, etc. Yet, of course, names can mean a great deal, rightly, wrongly, or falsely. Incidentally, the “wherefore” is sometimes mistaken to mean “where are you?” (People hear the “where” but not “wherefore” meaning “why”). Hope this is fairly clear?