Sorry to necro.

'Yin' was the name of the Middle to Late Shang capital, located near the modern city of Anyang, in Henan province. This is attested to by oracle bones and the few histories that detail the Bronze Age dynasties.

As for why naming conventions are different, it might have something to do with the historical documents used. The Shujing uses 'Shang' to refer to the polity and people, whereas the Shi Ji uses 'Yin'. What follows is conjecture: the archaeologists and historians who began the Japanese study of ancient China may have drawn heavily from the Shi Ji in their research, leading to an academic precedent to continue using 'Yin' in their writing.

Could it be because of the Kanji of Shang?

商朝

朝 -> North Korea​ Abbreviation

​

​

​

If you can write that question in Japanese for me, I'll try to ask my Japanese friends.