Fun character names include "myself" and similar, "you", "OMG!" and other interjections, "d00d" or just "dude", and a single space. For even more fun, hack some control characters in, so your name is a beep or something.
In Final Fantasy you could hack your name to be "OWOWOWOW", and in G/S you could insert variables such as the name of the last Pokémon you used in battle, the first one in your party, your rival's name, and some characters that expand to words, so you could for example name yourself TRAINERTRAINERTRAINERTRAINERTRAINERTRAINERTRAINER and break the formatting every time it's used.
More fun can be had in specific games, such as naming yourself Zelda in Ocarina of Time, and meeting her for the first time. "Zelda? That name sounds familiar..."
I used Hyper on my first run through Chrono Trigger, which got an O.o out of me when a chef offered "Hyper Kabob"... fun coincidence.
I always thought "???" as the rival in G/S might have been an oversight in the design, as it seems to be the default name until you change it. I wondered if they just didn't realize they were using his name in the dialogue before it was known.
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