In Chinese custom, no one changes his own surname unless married into the wife's family. This was quite different during the Ming Dynasty. Ming emperors gave out the royal name 朱 like candies, and the new 朱s in fact enjoyed special privileges. This renaming had also resulted in an unprecedented upsurge of the 朱 population in China.
By the end of Ming Dynasty, there was really no more privileges to enjoy. 隆武帝, who gave not only the 國姓 to 鄭成功 but also his new given name (in 1645, while lamenting that he did not have a princess for 成功 to marry to), was captured a year later by the Qing and committed suicide by starving himself to death. This had effectively ended the the practice of royal renaming and the prestige associated with it.
鄭成功 had never referred to himself as Koxinga or 國姓爺, that was the Dutch and the common folks, respectively, that did. It was still an honor as far as the Cheng Clan is concerned.