hi, let's suppose you're a chinese whose name is 司阿丽, one day, you come to japan. on your passport, your name should be also written in the roman alphabets as SI ALI.
in japan, since 丽 is not used in kanzi(japanese characters) and it cannot be typed under japanese language input mode, you should use traditional chinese character 麗 instead of 丽 in your daily life.
usually, japanese people will ask you how they should call you, if you say your name in chinese pronunciation, then they will write down your name's pronunciation using katakana as スー ア(-) リー and that would be SU ARI in the roman alphabets, and people will call you スーさん.
but in some cases, japanese people will pronounce your name as シ アレイ (in the roman alphabets, it's SI AREI) according to japanese style of pronouncing chinese characters. then you'll be シさん.
i think that should be enough for your question. but i recommend you to change your japanese surname. why? let me explain it for you.
in chinese, the surname 司 is ok, but in japanese style pronunciation, it's pronounced the same as 死(し), and 死 means death!
so, how about use 席(xi) as your chinese surname(it's second tone: /)? its pronunciation is close to your real name too. if you wish to own a matched japanese surname, this one is for you: 関, which is pronounced as せき(seki), it's actually being used as a surname in japan. 席 and 関 are both pronounced as せき in japanese.
席阿丽(XI ALI) for your chinese name, 関阿麗(せき あれい,SEKI AREI) for your japanese name, hope you enjoy them!