Did Katniss remain true to her identity once she arrived in the Capitol up until the end of the hunger games?

Yup, Katniss is pretty much a static character in that way. She is certainly a round character with strengths and insecurities that make readers like her so much. Katniss remains this way and doesn't fundamentally change whether she is in the Capitol, the games or District 12. She has different fears and doubts but she always remains Katniss.