Hey all,
I finally figured out a fix for myself.
I had iCloud turned on for all devices, everything seemed to be synced up, the country code didn't do anything for me...
I realized, looking through my contacts on my Mac, that my iPhone wasn't syncing all of the numbers and contacts I had to iCloud.
In other words, there was a contact card on my iPhone with a number, but it wasn't showing up on my Mac or on iCloud.com.
Those numbers that were not synced, consequently, were the no-name numbers in iChat, where only a number would display instead of the contact name.
Turns out, Messages, or iChat, only use contact cards stored in gmail.
FIX:
On the iPhone, go to:
Settings > Mail, Contacts, Calendars > (scroll down to "contacts" subcategory) Default Account > iCloud
(I had gmail selected previously, though I never selected gmail over iChat so I don't know why my iPhone was configured this way.)
Finally, you will then have to remake all of the contact cards that were not originally made in iCloud. All of the numbers that were showing up, instead of names, in Messages, were all contact cards I had made with this gmail default account. Unfortunately, iCloud didn't import the contact cards automatically from gmail.
A simple solution to this is to export your cards from gmail, then import them using your Contacts app on your Mac.
Voila! All my messages have a name to them now!