0 1. Li, the founder of the later Tang Dynasty, is not surnamed Li.
Li's grandfather, Li, formerly known as Zhu Xiechi, is the head of Shatuo from generation to generation. Later, due to his great contribution, he was specially named Li Wei. From then on, Zhu took Li as his surname. Even though he was suppressed by the courts in Tang Xizong, he and his son Li Keyong were forced to run to Tatar without changing their surnames. After Zhu Wen usurped the Tang Dynasty, Li Keyong, who inherited his father's footsteps, refused to recognize the legitimacy of Zhu Wen's regime and always obeyed the Tang Dynasty, fighting Zhu Wen in the name of restoring the Tang Dynasty. After his death, his son Li proclaimed himself emperor, taking Tang as his country name, claiming to inherit the orthodoxy of Tang Dynasty, that is, the later Tang Dynasty.
Therefore, Li's later Tang Dynasty actually had nothing to do with the Tang Dynasty. He was only a separatist force in the late Tang Dynasty, not an imperial clan named Li. It's just that taking Tang as the title of the country is beneficial to win people's hearts and attract the adherents of the Tang Dynasty, and it also has an excuse to declare war.
02. Li Bian, the founding emperor of the Southern Tang Dynasty, was not descended from the Tang Dynasty.
Li Bian's surname was indeed Li, but later he changed his surname to Xu Zhimo because of adoption. His father, Li Rong, came from humble origins and has no fixed address. Because of the years of war in the late Tang Dynasty, he wandered around with Li Bian, and later he was separated from Li Bian's mother and son, and his whereabouts were unknown. After Li Bian was adopted by Xu Wen, the general of the Southern Wu Dynasty, he gradually accumulated his own power as an adult. After Xu Wen's death, Li Bian took charge of the state affairs, and soon forced the Southern Wu Emperor to meditate and establish the State of Qi.
After two years as Emperor of Qi, Li Bian decided to change his name from Xu Zhimo to Li Bian, claiming to be the fourth generation grandson of the Tang King, and changed his title to Tang as the legitimate heir of the Tang Dynasty. But in fact, after becoming a king, it is even more unreliable than after Liu Bei, Zhong Shan and Wang Jing. But the emperor said that the courtiers had to believe this, so the Southern Tang Dynasty was born.