I know how to read hiragana and katakana, but know nothing else. A lot of people I know want me to write their names in Japanese. Is it right to write them in any system, or are there specific rules?
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Names of Japanese people have a specific spelling that may be in hiragana, katakana, kanji, or any mix thereof. You should spell their name as it is spelled, e.g. 「田中けい子」 (TANAKA Keiko).
Names of foreigners are written in katakana, unless they have decided on the equivalent kanji they want to use. Or if they ask you to choose the kanji then do so paying attention not only to sound but also meaning when selecting them.
You should keep in mind writing non-japanese names with kanji COULD be seen as somewhat not in very good taste. While it's there's no universal rule about it, since some people might see it as ranging from childish to culturally-insensitive, I'd keep using exclusively katakana for foreign names.
Straying a little from your question, it's generally a nice idea to write names in whatever script and with whatever spelling they originally are whenever possible.