The gamepedia page says that there are eight prefixes and eight suffixes that indicate particular affixes (Fast and Frozen).
+-------------+-----------------------+
| Fast |
+-------------+-----------------------+
| Prefix | Suffix |
+-------------+-----------------------+
| Valafar | Swiftspite |
| Breakneck | the Quickened |
| Kazfiel | , Dispatcher of Faith |
| Hastus | Siezefrenzy |
+-------------+-----------------------+
+-------------+-----------------------+
| Frozen |
+-------------+-----------------------+
| Prefix | Suffix |
+-------------+-----------------------+
| Deumos | the Embalmed |
| Marax | the Ice Lord |
| Chulock | Winterfang |
| Shiverstark | Soulfreeze |
+-------------+-----------------------+
So if you see a rare named Alot Swiftspite, then you know that it has the Fast affix. Similarly Chulock, Crippler of Princes would have the Frozen affix. I suppose that Kazfiel the Ice Lord would be both Fast and Frozen. Not sure if that ever happens.
That page also has a long list of prefixes and suffixes that it says are randomly assigned and mean nothing.