"Logo", primarily, may not have been the most accurate word to use. What I'm thinking of is something along the lines of a "mark", or a "symbol". Something that you can leave in place of your name, and for people who know your mark, that would be as good as a signature. Very similar (identical, in fact) to the way a chop is used in China or Japan.
So this would be my own mark for personal use on all kinds of stuff. Correspondence, stationery, the back of business cards, burning into people's foreheads after justice is served(PUM!); stuff like that.