Typically, but it depends. Zainichi Koreans tend to pick up local names because the xenophobia otherwise makes things very difficult, but they aren't really foreign, per se, except in their treatment by the state and people (most, if not all, were born in the country). Chinese people may also switch over from writing their names with hanzi to kanji for simplicity, but that's not really often, either.
Also, it was kinda funny when I actually tried to parse out how Nemi~ picked that particular kanji. That...kinda isn't really common name kanji.
へ へ
の の
も
へ
Can't do the ji part large enough...