Taizi

Taizi (Chinese: , "tàizǐ", "Supreme Son") was the title of the crown prince of imperial China.
Succession.
Traditional Confucian political theory favored strict agnatic primogeniture, with younger sons displaying filial obedience to the eldest upon the passing of the father. This rather straightforward system was somewhat complicated by polygamy: since later wives were subordinated to the first, their children even when born first were likewise subordinated to hers.
Following Lu Gu's conversion of Liu Bang to Confucianism in the early 1st century BC, Chinese dynasties observed it in theory though not always in practice. Liu Bang himself began to favor Concubine Qi, a later concubine, to his primary empress, Lü Zhi, 
and doubted the competence of his heir Liu Ying. Even worse conflicts could occur when invaders previously observing their own rules of inheritance began to sinicize, as happened to the 10th-century Liao dynasty.
Under the Ming Dynasty, the traditional Confucian principles of succession were upheld by the Hongwu Emperor's "Instructions of the Ancestor of the August Ming". These presented a grave problem when his eldest son died early, leaving a power struggle between a sheltered teenage grandson and his many experienced and well-armed uncles. One of these, the Prince of Yan, eventually overthrew his nephew under the pretense of saving him from ill counsel. His own legitimacy was precariously established: a charred body was procured from the ruins of Nanjing and proclaimed to be the accidentally-killed emperor; the nephew's reign was then condemned and delegitimized and the surviving son kept imprisoned and single; and imperial records were falsified to establish the Prince of Yan as his father's favorite and as a son of the primary wife, giving him primacy over his other brothers.
Names.
As "taizi", the crown prince would possess a name separate both from his personal name and from his later era name, temple name and posthumous name.