Some I've seen over time - most are/were not my own:
The Gnome Alaska
Stilth Incan* (I-as-DM ask player for PC's name; his reply is "still thinkin'"; my reply is "Good. How are you spelling that?")
No'ei Deyayet* (same sequence as Stilth, above)
Axwell Smart (not a PC name yet; I use it for one of the warriors a PC of mine has the ability to summon now and then)
Characters with dismal starting stats have generated a few:
Mediocrates^
Averjax^
Knottwoor Thmutch
Weir Foct
^ - fun fact: Mediocrates and Averjax came into a party together; Mediocrates lasted just long enough to be caught in the only TPK I've ever DMed.
Class-race combinations have led to:
Pelmuc (Part-Elf Magic-user/Cleric)
Anne (Assassin-Necromancer Neutral Evil; killed in process of meeting the party before they ever knew what she was)
Elena (Elf Lawful Evil Necromancer-Assassin; and Anne's direct replacement)
Our random name generation system has led to some crazy and-or nigh-unpronounceable names; one of the worst of the latter being my bard Que'fnlnrl. Oddly enough, her name being unpronounceable made sense in a way: she was a full Dryad, meaning the only way to say her name properly would be to first turn yourself into a tree...

For day-to-day purposes we just called her Ka'fell.
And the worst: I once ran a one-shot where one of the players was named Bernard. A different player named her character Bernard. What a nightmare
that was!