Actually, parrots have a better understanding of human speech than we think. They can not only learn words, but they can learn how to use them in context, so they actually understand the words they pick up. While they may not have the same vocabulary range as we do, they are able to understand.
Also, parrots are actually able to learn their names, just like how dogs may learn their names, and you can use that for more advanced flight recall, where they will fly to you when you call them. While they're better with visual commands, they can understand verbal commands quite well when trained enough. When in the wild, parrots actually have certain "names" which is a certain series of calls. They learn it from their parents, and their siblings, and they know who talks to who in the flock. I think we just have the tendency to give them human names as pets, since it's easier to pronounce.

But some people don't name their birds, so you don't really have to. I guess it just gives a sense of identification for most owners.