What is the origin of Song Wu's nickname in Water Margin?

The origin of Song Wu's nickname in Water Margin is:

Song Wu's nickname was "Monkey", which was a name for Taoist travelers at that time. He is a hero who killed the tiger, but his eldest brother was poisoned and very angry. After escaping, he met his sworn brother Zhang Qing and his wife Sun Erniang.

In order to hide people's eyes and ears and prevent Song Wu from being captured by the imperial court, he disguised Song Wu as a walker, wearing a gold hoop, tattooed hair, wearing a Taoist robe, holding a Buddhist monk's knife and carrying official documents. Later, he did evil deeds, went to Erlong Mountain, joined forces with Lu, and finally went to Liangshan together, and continued to use this ancient costume image to uphold justice for heaven. Since then, Song Wu has formed a nickname of Walker.

Character introduction:

Song Wu is an important figure in Shi Naian's classic Water Margin. It also appears in Jin Ping Mei, because it ranks second in the family and is also called "WuErlang". In order to avoid being arrested by the government, he dressed up as a monk and was called "Monkey Song Wu" by Jianghu people.

Song Wu once killed a white-fronted tiger with his bare hands in Jingyanggang. Therefore, the story of "Song Wu killed the tiger" was widely circulated in later generations. He once gathered with Lu, Yang Zhi and others in Erlong Mountain and Sanshan Mountain in Qingzhou, and surrendered to Liangshan, one of the top ten generals, and ranked 14th.

After being embraced by the imperial court, he conquered Liao, Wang Qing and Fang La with Song Jiang. He was eventually injured by a flying knife in the process of collecting Fang La, lost his left arm and was named the founder of Zhong Qing. Finally, he died in Liuhe Hall in Hangzhou, with a life span of 80.