Back when I first made my main on my server, it was around Halloween and I was looking at costumes. A beer wench costume caught my eye, and it became the inspiration for my name. Much later when achievements and many titles were introduced, I learned of the Salty title and knew I had to get it. Salty just goes so well with a wench name; I always go back to it after wearing a new one for a few days.
Names are a very key part of the game -- from the creation screen, titles, pets, renaming scrolls for pets, guild names, and paid guild/character name changes. You can now even pay gold to change your warlock demon's name, if you wish.
Either I'm not very creative or I just like to honor the beast, but if I tame a rare creature that comes with a name, I rename it back to the original. It would be neat if there were an option to either keep the name or rename it, since some names you can't emulate exactly.
There are some creatures out there that I wish could be named or renamed -- a mage's water elemental, for example. It would be nice if something that is with you from day one could have a unique name, similar to warlock demons and death knight minions.
What was your inspiration for your name? Is there a title that was a perfect fit? Have you renamed any of your pets, demons or mini-pets, or do you keep their original names? Do you wish you could name something but can't yet?