You cannot name pictures in the Photos app. However, you can group pictures in a folder that has a name. Plus, if you share photos using Photo Stream, you can add a comment or name to a specific photo. Hope this helps.
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I have renamed photos in Documents 5 as well as in a photo album app called MyPhoto. What seems to happen is after renaming, the photo retains the new name while in that app, or after sent as email. But once the image is saved to the camera roll, the name reverts back to something like IMG_8769.JPG. The camera roll kills the name. I can also rename photos in Box. I don't see that option in Dropbox. So I save a named photo from Box back to my camera roll, then upload it back to Box. The name is then gone. So to keep an image named, don't save it to the camera roll.