I think that identity is seen in the drama as a social construct that individuals must actively combat in order to discover their true sense of self. This is operating on the premise that Romeo and Juliet did in fact love one another. If one accepts this, then it becomes equally evident that the acceptance of their love is a repudiation of socially constructed notions of identity.
The social constructions of identity are ones seen in the opening moments of the drama. Identity in Verona is drawn along socially established lines of who is a Montague and who is a Capulet. There is no other identity than social affiliation. The relationship that emerges between Romeo and Juliet is one in which identity is constructed outside of social affiliation. This is why they struggle so much. They seek to find an identity outside of "Capulet" and "Montague." Their escape plan is rooted in this idea. When Juliet breaks the bonds with her parents in Act III, sc. 5, it is a moment where her identity is outside socially established contours. The reason why her parents are so harsh to her in this scene is because she seeks to exert an identity that is opposite of what her parents wish. Identity is shown to be a reality that individuals must actively embrace, which, at times, requires individuals to break down socially dictated notions of the good. The reason both lovers struggle and eventually die is in their desire to find an identity that is their own, apart from that which is socially manufactured.