Since kanji can have multiple pronunciations, how would you know how to write someone's name if you've only heard it spoken? What's the convention? Would you just guess, or maybe write it out in hiragana instead?
It depends on what you're writing, I would think. If you're writing a note to yourself, like "Call Suzuki-san later", of course you could guess or just write it with kana.
If you're writing something to the person themselves, I tend to write it in katakana. I don't know why, but this seems to be politer, in a sort of neutral way. But this is just my inclination and there may be no truth to it.
If you need to write it in some kind of official document or paperwork, you should probably just ask the person how to write it. If you can't ask the person directly (like a historical figure, etc.), chances are someone knows how it is written. If not, hiragana would probably be an OK fallback if there's really no way to figure it out.
Also, there are some people who have no kanji for their first name, so in this case you'd use the hiragana.
Whenever I've been in this situation, it's only ever been when writing notes or informal emails to friends, and I've found that I can get away with using Hiragana evertyime. but I like to surprise my friends with the correct Kanji every so often (followed by a "Did I use the correct Kanji for your name?" type question as a post script to the note/email).
I've always made a point of asking new Japanese people I meet which Kanji to use in their name when I meet them. When I have to ask them in English, however (usually due to forgetting how to ask in Japanese) I fall into the trap of using the following sentence (I blame my Japanese teacher):
How do I spell your name with Kanji?
This is because my Japanese teacher, when introducing new Kanji would say things like "This is how you spell the Kanji," rather than "This is the stroke order [for this Kanji]".
I'm not sure how you would go about this in a business/formal environment. But I suppose that if you've met them in this environment, they've probably produced a 名刺(めいし) for you at some point. I have noticed that some business people who have "complex" Kanji in their name tend to have Ruby text/Furigana along with their names to aid in reading them.
I've noticed the above a lot when meeting Japanese people where I work (in the UK). The 名刺 they usually present will have Japanese (with Ruby text/Furigana) on one side and English on the other (in the same order and format).
I have, on occasion, asked (very politely) for the person to read the Kanji on their 名刺 to me (if they don't mind), and when I explain that I'm always looking for new Kanji and vocabulary to learn they usually oblige me with a quick reading of the characters. I don;t know whether this is considered good form when meeting new people, though. But it seems to fit nicely with the "If you're not sure, ask someone" attitude that I was raised with.
I know that this doesn't answer your question exactly, but I thought I'd share anyway. My rule of thumb is, when in doubt use Hiragana (and ask the person which Kanji to use for next time).