I have to admit I was a little confused when I asked this question, as I thought that it was my Gmail where names and email addresses were connected.
But of course, it's not the local Gmail client that attaches a name to an email for display when receiving, it's whether or not the sender has a name attached to their email, as explained in the answer.
Okay... but, can I set Gmail up in a way so that it will replace a known email address with the name I have for them in my contacts in situations when someone sends me an email with no name set? Or, even better, over rides their name with the one I have set in any case (since I think of them by the name I have set, not what they have set)?
This is standard practise when it comes to phone numbers - when someone calls my Android phone, I see the name that I have set in my contact list. Hopefully this could be done with emails as well.

.I've contacted them obviously and told them to fix it, but it would be nice if Gmail would do it for me. – Larry Aug 10 '12 at 14:03