For example, Lee Jun-ki (이준기)'s name uses the following hanja:
In Chinese he'd be called Li Zhun-ji, which is just the straight Chinese reading of the characters.
Same with Japanese names, such as Shiina Ringo (椎名林檎):
In Chinese she is referred to as Zhui-ming Lin-qin.
How are Chinese names referred to in Korean and Japanese? I guess in Korean, they just use the Korean reading? I've checked some Wikipedia pages of notable Chinese people in Korean and Japanese, and usually I see a phonetic transliteration and the Korean/Japanese reading in parentheses. For instance, Mao Zedong is listed as 마오쩌둥(모택동). The bolded part sounds more like "Mao Zedong" in Korean, but the parentheses is how the characters for his name would be read.
Then there's Chen Ken'ichi, whose name works out in both Chinese and Japanese.
When read in Chinese, it's Chen Jianyi, and when read in Japanese it's Chin Ken'ichi.
Basically I'm wondering what kind of standards there are for names across these Chinese-character-influenced languages. For example, a Chinese living in Japan ... would he use the straight Japanese reading of his name like Chen Ken'ichi? What if the characters are really rare and don't exist in Japanese? Would he adopt a new but similar name that works in Japanese? Which reading is chosen for these characters?
How would you render my name in the three languages? (I'm an anomaly though, because my surname is Chinese and my first name is Japanese.)