I'm the one who answered the question mentioned in your question. I think I have to make a clarification fist. I think you misunderstand that question. The poster is asking how to choose Chinese characters for a Chinese name if a foreigner wants one, not how to "translate" a foreign name into Chinese. They are different.
As for your specific interst in how Japanese names are mapped into Chinese. Here is my two cents.
Due to historical reasons, Chinese language and culture deeply affect east Asia, more specifically, Japan, Korea and Vietnam. Among them, Japan still perserves many Chinese characters (Japanese, 漢字{かんじ}) in Janpanese language. In many cases, a Japanese name fully consists of Chinese characters, so it's would be straightforward to keep the name the same when "translated" into Chinese. In few cases, when the name consists of some hiragara/katakana (Japanese,平仮名/片仮名; Chinese, 平假名/片假名), a character commonly used in names would be chosen to "translate" the Japanese name into Chinese character, as Tangho pointed out. Some exapmples:
安室 奈美恵{あむろなみえ Amuro Namie} (a female Japanese singer) in Japanese = 安室 奈美恵 in Chinese
初音ミク{はつね ミク Hatsune Miku} (a virtual figure famous for "her" singing) in Japanese = 初音未来 in Chinese, since ミク is the nanori (Japanese:名乗り, a special pronunciation used in Japanese names) of Chinese characters 未来.
長渕 剛 {ながぶち つよし Nagabuchi Tsuyoshi}(a male Japanese singer) in Japanese = 长渊 刚 in Chinese. Here, Standard Chinese characters in Simplified Chinse are adopted after the "translation".
Of course, in case you just want a Chinese style name even when you are a Japanese, you can "arbitrarily" choose your Chinese name.
By the way, for Korean and Vitamnese, they have their name of the "version" in Chinese characters, so their name always looks like an original Chinese name. No "translation" is needed.