Following Hong Kong tradition, married women may prepend their husband's surname to their maiden surname - Carrie's husband is Lam Siu-por
林兆波, her maiden surname is Cheng
郑. Hence
林郑月娥 /
林郑 in Chinese, 'Lam Cheng' in English. This dual-surname form is a Hong Kong / Macau / Cantonese-diaspora convention rather than mainland practice.