Final answer:
Romeo discovers Juliet's last name through her nurse after the Capulet's party, revealing she belongs to the rival family of the Montagues.
Step-by-step explanation:
Romeo finds out Juliet's last name through Juliet's nurse. After meeting and falling for each other at the Capulet's party, Romeo is desperate to know who Juliet is. He is unaware initially of her family background. However, he stays after the party to catch another glimpse of Juliet and ends up overhearing the nurse call Juliet back into the house, referring to her by her first and last name, Juliet Capulet. This revelation is a shock to Romeo since the Capulets are the sworn enemies of his own family, the Montagues. From this, the central conflict of Shakespeare's Romeo and Juliet arises—it's a classic tale of love caught between feuding families. The whole situation is embedded deep within the motifs of fate and the folly of hate, as this newfound knowledge sets the stage for the tragic events to come.