When you're looking at your photos so that there are a bunch of them tiled across the screen, do you see the photo name under each photo, like "IMG_1234"? If not, turn this on by clicking View->Titles. Then to name a photo, simply click on that filename ("IMG_1234") and type in a new name.
Another way to do it is to select a photo and click the Info button. This will open up an info pane on the right side of the window. From there you can give the photo a name and also key in a description.