When you join Xbox Live you will need to create a gamertag, or virtual name tag, that will span all your games on Xbox Live and games for Windows Live. Your gamertag is linked permanently to your account and will display your game achievements, gamer score and Xbox Live profile. Depending on your preferences you can select a gamertag to show other gamers a little bit about yourself.
Irony has its place in the gaming world and you can use your gamertag to create an ironic "persona." If you are a multiplayer game buff, a gamertag like "fluffybunnypants" can be fun if you are very good at the game. In a first-person shooter, nobody likes to see a message scroll by like "Fluffybunnypants just shot you in the head."
If you are confident in your game-playing abilities or if you're terrible and just want to sound menacing, you could select a gamertag with an aggressive tone. "Headshotspecialist" would strike fear into the hearts of FPS gamers and "Powerleveler" might make MMO players scared to duel you.
You can find other gamers with similar interests if your gamertag is related to your favourite hobbies. If you go with "Joetheskater" you may come across other players interested in skateboarding and quickly develop a large list of friends with similar interests to play with.
Game Specific Gamertags
If you only plan to play a certain genre of games, a specific gamertag can be very recognisable to other players. "Sniperbob" may quickly build up a following on games such as "Halo" or "Call of Duty." It's short and easy to remember.
Avatar Based Gamertags
You can create your gamertag to represent your avatar's appearance on Xbox Live. If you plan to dress your avatar in royal garb, "KingGeorge" could work. If you will wear a gas mask and a kilt, maybe "TheGassyScot" or something similarly strange. Keep it clean and non-racist or your gamertag may get banned, taking your gamerscore with it.