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This one doesn't really count since I actually wound up using it, but I played a fat, lazy halfling wizard named Provalor the Proficient. He was a blast to play, being, well, proficient.
It was more of a limited imagination than a joke (and a bad one at that), but I had a player who insisted his wizard's name was Wizard. And he kept calling himself "wizard Wizard" or "Wizard, the wizard"...
You know, I DM for Atlatl... when he's playing Atlatl... and it never once occurred to me that the name was a reference to Chucker Jones on M.A.S.H (and I watched a lot of M.A.S.H as a child).
There's a fine, well, non-existent line between my joke and serious names. That said, I really want to play an alcoholic Jedi Knight (based on Peter O'Toole in My Favorite Year) named Ginn Gimlet and a hermaphrodite child-soldier from an alternate universe (who fights crime in ours) called Vivian Girl.
Whenever I run Undermountain, my players betimes run afoul of the Xanathar's chief rival for beholder crime lord, the Notorious E.Y.E. That's an ancient gag and for an NPC though, so I'm not sure that it counts.
A recent South Park episode and the release of Player's Handbook 2 has inspired me to design a kuo-toa bard named Eynak East.