Usually it's "Halfbeard" (go figure). When I was younger and first started growing facialhair, it grew in thicker and darker on one side. My godmom's brother christened me as Halfbeard and said it sounded like a medieval warrior's name: "Halfbeard did good in battle today."
Demi Lovato, haha. My usual character name is Demesne, and no one can ever pronounce it correctly, so one day, one of my friends was struggling to say it, and just yelled "Demi Lovato!" It's been my nickname since(Although sometimes it's just 'Demi.'
I really just use a bunch of random ones. I do still have my original names from the games that I started when I was a lot younger, but the newer ones are just a collage of different names. It is a little different when you are using the games to communicate though, because sometimes my friends have multiple names too so it can get confusing.
I try to pick names that are unique and often available such as StormiRayne or GenaJade. I also feel like it makes my characters stand out and the names are often easier to shorten, which sometimes drives me crazy. I have some games where I use the same name over and over, but for the most part ,I use creative and unique sounding names. One of my most unique that I came up with was KloeHayze, which is a panda in World of Warcraft. Other people made Asian themed names and it just became monotonous and repetitive for me.
I should also add that it does depend on what particular class I am creating as well. For example, my lock is named StormiRayne because she makes it rain fire with her Rain of Fire spell. I found that it fit the class itself so I picked it. I don't always use this tactic, but it does come into play in certain situations.
A nick name for my characters would usually be my nick name in real life. If not that then usually a color or an element of some sort.
I choose my character's name close to my own name--like my nickname. I want to feel like the character really represent me. Sometimes, I choose my character's name basing their job--like my character is a support hero, I named her "helpinghand". I really think carefully on what will I name to my character, it motivates me more in the game.