Must Japanese people's name be mapped to equivalent Chinese characters?
Yes, if a Japanese name can be written in kanji, it is customary to read these kanji in its Chinese character pinyin, the Japanese pronunciation play no part.

The Japanese pronunciation of "田中" is "Tanaka",  But 田中 in Mandarin is read as / tian2 zhong1/ using Mandarin Pinyin and    /tin4 zung1/ in Cantonese using Cantonese Jyuping

If you are a Japanese named 田中 (Tanaka), your Chinese name should always be 田中 (tin4 zung1) also. Picking a different Chinese name, for example 田 (tin4) so your name can sound more Chinese, is considered insulting to your heritage.

Some Japanese first names do not have fixed corresponding Kanji, for example  あかね (Akane).  In this case, we have to choose among all the Kanji that is pronounced  あかね,  and 茜 is the most common one.