Hi Phil,
No, it is announcing them backwards - ie surname, first name. Per your experience, changing the name order in the iPhone settings menu appears to have no effect on this.
I would imagine the reason for this is that the when the contacts are uploaded, they are processed in a certain format that cannot then be changed without re-uploading them. If name order is important to you I would suggest resetting the ST3, then changing the contacts order settings on your iPhone, then re-pairing/re-uploading your contacts. You many need to try this a couple of times to find the right combination of "sort order" & "display order" (the 2 contacts options on the iPhone).
If you do try this, can you please be sure to post your results here?
Cheers, Andy