The first answer I got is that he is called "Q" because he is cute and "Q" sounds like cute. This didn't seem to hold much water, but I recieved this answer from two or three people. Others didn't even hazard a guess. Some confirmation of this "cute" origin came when I located a Lao Fu Zi animated cartoon on Laser Disc and rented it. This was "Lao Fu Zi and E.T." (you can see how Lao Fu Zi crazy I was, and obviously still am since I'm doing this web site.) The computer print out of the receipt had the English name of the movie as "Old Master Cuter" (yes, "cuter", not "cute". This is not a typo.) This seemed like confirmation of the cute origin of Old Master "Q" .
But, later I found what I think is the true origin of the "Q". I ask the "Q" question of a friend of mine from Hong Kong. He said he thought it was probably based on a story called Mr. Q. He said it was in their text book at school and everyone had read it. The story he is referring to is The True Story of Ah Q by Lu Xun. I asked another friend (this one from mainland--where Lao Fu Zi is not so well known) and he said that he believed that the "Q" comes from Lu Xun's Ah Q story. He thought so because the Ah Q story is quite humorous.
If you are familiar with the story of Ah Q and also with Lao Fu Zi comics you'll notice that the similarities between the two aren't all that strong. Ah Q is much more of a tragic and inept fellow. His unwarranted arrogance and general ignorance is a major part of the Ah Q story. Lao Fu Zi on the other hand is a pretty cool character who can do so many things. But comic strips evolve and in the beginning Lao Fu Zi may have been more like the clueless Ah Q. The irrational belligerence and fighting between Ah Q and others is probably the main similarity that can be seen. Take for example this vignette from Ah Q and compare it to this Lao Fu Zi comic.
So the mystery of where the "Q" in Old Master "Q" comes from was solved. But what intrigued me was the high regard my friends had for the author of the Ah Q story, Lu Xun. I recieved comments like "I studied his writings" and "I have all his collected works back home in Beijing". My interest was piqued.