how does hamlets and rosencrantz true colors emerge?

Hamlet- Hamlet takes a while to show his "true colors" because he spends much of the play trying to figure them out. He berates himself for his inaction over his father's death and his mother's sexual indiscretions. In the end, Hamlet finally does get his day of reckoning but his "true colors" remain similar to when we first met him. Hamlet remains the thoughtful reflective melancholic Dane even at his death. 

You need to ask about Rosencrantz separately.