I've given my rival so many different nicknames over the years. Besides the obvious ones we all did as kids like "Poop" and "Stupid" or anything along those lines, I usually named my rivals after other people I knew who played Pokemon.
Originally it was after my younger brother, Triton. Then it was probably either Greg or Lawrence - my two childhood best friends. And then after that, I think i stopped nicknaming the rival for a long time, until recently. Now I usually name myself after drag queens or Lady Gaga (my true original stan), so my rival gets nicknamed after someone that queen has had a fight with (or who sent them home in a lip sync), or it's Madonna since she hates Queen Gaga (before any fellow Little Monsters hate me, I still like Madonna).