1. Kanji with Chinese character counterpart
Wikipedia (ref 1) implies this is the majority case:
Japanese names are usually written in kanji, which are characters usually Chinese in origin but Japanese in pronunciation.
When translating these names, the kanji characters are directly converted to their Chinese counterparts. It's not always 1:1 though, like both 沢(kanji) and 澤(kanji) map to 泽(Chinese character).
2. Kanji without Chinese character counterpart
Wikipedia (ref 1):
Sometimes, a Japanese name includes kokuji. These kanji resemble Chinese characters but originate in Japan and do not have Chinese pronunciations. For example, the word komu (込) has no Chinese reading. When words like this are encountered, usually the rule of "有邊讀邊，沒邊讀中間" ("read the side if any, read the middle part if there is no side") applies. Therefore "込" is read as "rù" which is derived from 入.
This paragraph implies these kokuji are not translated, instead, Chinese pronunciations are 'invented' for reading.
On the other hand, the Zhihu Q/A (ref 3) suggests
In practice we see all different methods being used even in formal occasions (like broadcast and newspaper). No single rule is strictly followed.
3. Hiragana and katakana in names
From real life cases we know this is the place with the most flexibility. One thing I'm sure is the hiragana or katakana have to be translated into Chinese characters, but methods may span 'best guess' kanji conversion, direct paraphrasing, contextual paraphrasing, transliteration (rare), etc.
As mentioned in ref 3, when it comes to ACG (Anime, Comics and Games) or any fictitious names, it's free translation. Examples:
例如：アラレ → 阿拉蕾（原词为放在拉面里面的小号膨化颗粒）
例如：ナルト → 鸣人（原词为拉面上面放的鱼饼，常画有粉红色的螺旋图案）
例如：ピッコロ → 短笛（就是乐器短笛的意思）
例如：野比のび太 → 康夫（原文翻译，用填补汉字的方式应为野比延太或野比伸太）
For real person's names I believe 'best guess' kanji conversion is the most common method, with which there is still a lot of flexibility (or say lack of standard) like you said in your question.
E.g. '沢尻 エリカ' (Japanese actress) does not have kanji for her given name and used to be translated as '泽尻 绘里香' as 'best guess kanji'. Later the actress herself picked '泽尻 英龙华' (which has the same pronunciation) as the 'official' kanji name (reference here).
BTW, for Yoshi in your question, I believe the most common 'best guess' kanji is 吉.