A cool username is easy to remember and sparks interest in your posts. To find one, you should understand your audience, seek inspiration and do your research. For a Jazz music forum, for example, you could draw inspiration from the history of Jazz. For an artist or celebrity platform, you could research an artistic style or tool used in the medium, or a famous incident in the career of the celebrity.
Combine Ideas, Connect Concepts
No idea is too crazy when searching for inspiration. You could meditate on the subject or use random association -- write down ideas, names and associated topics, and connect them with arrows and symbols. Go for a walk; watch animals play. Write things down whenever they come to you and leave nothing out. Collect all of your ideas and examine them later.
Find Help on the Web
Websites like Spinxo, NameGenerator2 and MyUsernameGenerator use your input plus random word generation to suggest a username. You are the ultimate judge as to whether or not the username is cool. At the very least, you can use the username provided by these websites as a starting point to create one you like.
Beware of Unintentional Messages
Make sure to scrutinize your final choice carefully. Read it backward or cut it into pieces to see if it carries unintended messages. For example "IMTherapist" might be fine for an instant messaging forum, but this username is very close to "I'm the rapist," which would not be a cool username anywhere.