"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” (Shakespeare 2.2, 36-9).
Act 2 Scene 4
"Not to his father's. I spoke with his man" (Shakespeare 2.4, 3)
"Where the devil should this Romeo be? Came he not home tonight?" (Shakespeare 2.4, 1-2).
Act 2 Scene 6
"Come, come with me, and we will make short work, for, by your leaves, ...
...you shall not stay alone till Holy Church incorporate two into one" (Shakespeare 2.6, 35-7).
Romeo and Juliet want to rebel against their parents and refuse their names. Theu are much in love and are willing to go against their families. If they don't change their names, they will feel imprisoned if they stay together.
Romeo wants to stay with his love, Juliet. He doesn't want to go home, he jumped over a wall to be with her. He is forgetting about his family, and they must be worried. They think he has feelings for Rosaline, but they don't know that he actually loves his enemy.
Romeo and Juliet love each other enough to get married, despite knowing that their families have an ongoing fued. They want to be married and have different names. They hope their parents will be friends after they get married.