I have tried the procedure as suggested above, and unfortunately can confirm that it doesn't work.
Although I can transfer contacts to the ST3 from my Mac (or from a Nokia), it appears that the contacts are stored only with that phone's pairing, so when it is paired with the iPhone 3G it doesn't recognise the contacts and still reads out the number instead of the name.
The only thing I can think that might work is trying to trick the ST3 into pairing with another device "pretending" to be the iPhone, but that's outside of my technical skills.
From reading elsewhere, this appears to be an issue with the iPhone 2.0 software, so hopefully it will be fixed in 2.1 (ie. an iPhone with 1.1.4 works, but if it has been upgraded to 2.0 it no longer works)
Evidently this is causing issues with built-in BMW bluetooth as well.
If anybody finds a trick to get it to work, I'd be keen to know. It was one of the selling points for me for the ST3 over less expensive options - but on the bright side, I'm getting to know people's numbers again, as it reads them out 🙂