Which is the main star of Gemini?

The main star of Gemini is Beihe III, namely Gemini β, with a brightness of about 1.2, and Gemini α, namely Beihe II, is also very bright, with a brightness of about 1.7, making it one of the brightest second-class stars. The ancients classified Beihe II as α because Beihe II was brighter than Beihe III in ancient times, but now Beihe II is not as bright as Beihe III. It is speculated that Beihe II may be a binary star or a multi-star, with a long period of light variation and possible changes in brightness. It is not impossible to surpass Beihe III again.

Xuanyuan XIV is the main star of Leo, with brightness 1.35, etc. It is the darkest class, located on the ecliptic.

As for the planet Mercury, how does it become the main star of the constellation?