Is “How did Shoumeng refer to himself in diplomatic interactions with other feudal lords at the time?” true?

The Records of the Grand Historian, in the hereditary house of Wu Taibo, directly states in its genealogy: "Shoumeng, the nineteenth-generation descendant of Wu Taibo's younger brother Zhongyong." In the Chronicles of the Eastern Zhou Kingdoms, Chapter 58, in the context of diplomatic occasions with other states, it emphasizes his usurpation of title yet still being called 'Wu Zi': "Having learned that Wu Chen had gathered Wu Zi Shoumeng together with the high officials of Jin, Lu, Qi, Song, Wei, and Zheng at Zhongli, Gongzi Ce then persuaded the King of Chu, saying: 'The alliance between Jin and Wu will surely lead to plots against Chu.'"