What nomenclature do the star names "Beihe III" and "Betelgeuse" belong to?

The so-called Beihe III refers to the ancient name of Gemini Alpha, the brightest star in Gemini, China. In the naming method of ancient stars in China, the whole sky was divided into three walls, four elephants and twenty-eight lodges, which was the basic skeleton of the stars in the whole sky. The ecliptic is basically in 28 nights, and the three walls give the meaning of palace and harem, which is the residence of the emperor in heaven. In addition, among many other constellations scattered in Sanyuan, Sixiang and Twenty-eight Nights, ancient Chinese astronomers also named them according to their positions and imagination. The principle of naming is basically to move the politics, geography and history they saw on the ground to the sky and arrange the stars in the sky into the feudal kingdom in the sky. Each kind of star has more or less stars, which are distinguished by one, two, three and four. For example, Betelgeuse is the fourth star of Betelgeuse (of course, it has nothing to do with brightness), and Hegu II is the second star of Hegu II, also known as Altair; Beihe III is the alpha star of Gemini, so it is called Beihe, because this star is located in the north of the Milky Way and is symmetrical with the star in the south of the Milky Way. Others such as Nanhe No.2 Middle School, Wuche No.2 Middle School, Subi No.5 Middle School and Tianjin No.4 Middle School are all affected by this.