I go by avatar, and i often wonder when i see the same avatar on a different forum if it is the same poster as here. Forum names are so impersonal, i don't honestly believe that people are the names they say they are and often remembering some arbitrary string of letters is more difficult than going by picture.
Although I personally photoshopped my own avatar, and am fairly attached to it, its Bill from L4D if he were a cat by the way, i know that other people often just throw up a random GIF and change it every so often, or just take the name and picture a a fictional character and use that, making them difficult to identify.
I guess sometimes you need both.