Well, mine is kinda like inot2B's. I have a very large name, and one of the middle names is Alastair, which I started using almost exclusively back in 89 (there were just too many Michaels and Mikes at college). A friend of mine thought Alastair was too formal a name for our circle of friends, and shortened it to Ali, which stuck. Alicat was only a brief step away.
Now, my other alias, which I use at Yahoo, is persnikitty, and no, it was not derived from persian kitty, but persnickety, combined with my inherent feline qualities exemplified by Alicat. Ergo: persnikitty.