What were the individual family names of Shakespeare's Romeo and Juliet?

Romeo's family name was Montague and Juliet's family name was Capulet.

Explanation:

The Montagues and the Capulets were two rival families living in Verona, Italy. The Prologue of the Shakespearean play mentions their grudge to be an ancient one, having already made them shed blood, but offers no further explanation as to how or why it started.

Romeo and Juliet fall in love with each other only to find out that their love is forbidden due to their families' feud. Juliet, however, takes some sort of potion that lowers her heart rate enough to make her look as if she has died. Her plan is to free herself from her family by pretending to be dead and then running away with Romeo. She sends Romeo a letter but, unfortunately, the false news of her death reaches him before the letter does.

Romeo, who can fathom life without his precious love, kills himself by drinking poison. When Juliet wakes up and finds Romeo dead by her side, she stabs and kills herself with a dagger. Their tragic ending is the final lesson to be learned by the Montagues and the Capulets. If it weren't for their heartless grudge, their son and daughter would have been alive and happy.