Pet names for my cats worked a different way, than they do for Lizzie, my dog. Each of them had a primary and secondary nickname; Bugsy’s were Little Buddy and Little Guy and Casper’s were Casper Doodle (variant: Casper Doodle Do) and Casper Cat, then each one of them had their own nickname generating “system,” kind of a perpetual random nickname generating machine that always incorporated their real name. Casper’s system basically involved adding suffixes of some sort to his name like Caspership, Casperlicious, Casperness (that one led to the occasional Your Royal Casperness), Casperonium, Casperette, Caspericity, Casperfy, Casperize, Casperesque, etc. Bugsy’s system was basically incorporating his name into the names of real people (or fictional sometimes): Bugs Guevara, Bugsferatu, Vincent Van Bugsy, Albert Bugstein, Werner Heisenbugs, Tycho Bugsy, Humphrey Bobugs, Daniel Day-Bugsy, Alexander the Bugs, Teddy Bugsevelt, Mohammad Bugsi … well, you get the idea.
I also used to like giving them both random psuedo-Latin names like Casperius Casperatum and Bugsium Bugsorum.