Foreigners names are usually written in katakana, even if those names are Japanese in derivation (e.g., Americans of Japanese descent.) The names of Japanese and Chinese persons are essentially always written in kanji. (Kana given names on children's personal items being about the only exception. Family names are never written in kana except to provide the reading of the kanji.)
There are literally no rules about how kanji can be matched to pronunciation. There are common names, that everyone knows how they are commonly pronounced (but they often have alternate pronunciations too), and there are characters commonly used in names that usually have one or two commonly used pronunciations (sometimes the same ones as in words, sometimes a special 'name reading').
However, ultimately, the new parents (or someone changing their name) can put down any of the 2500ish kanji that are allowed by the government, in any order, and specify them as pronounced with any reading.