I think they do. I know they recognize the people who are kind to them. They certainly seem to know their names. My rooster Bradley will immediately stand up and beat his wings when I tell him he is handsome. My other roo Rocky will fly up into my hands when I put them out in front of him. I think much of it too is the tone of voice used. Birds can recognize when the tone of your voice is pleasant and when it's not.
Now remembering another chicken? That's intriguing question. I think they can. Here's why. I have brooded chicks together. Handled them, ect as pets. When they get old enough I move them to their respected coops. Sometimes I will need to remove a bird for some reason. I have noticed that even after time apart, sometimes even months, when I put them back together that bird that was removed is often greeted back into the flock. I've seen the pecking order at work with introduced birds into a flock. Birds will confront the newbie and get pushed around, feathers pulled until the new bird submits by wedging themselves in a corner and laying down flat. The birds that grow up together don't seem to do that. Often they just go about their business as if the one was never removed from the flock at all. It might also have to do with the breed as well. Some breeds being less agressive than others?