a) As a user, you cannot change the name on your user account.
b) If you wish to use a different username, you'll need to register again with the new name you wish to use. Note that each account requires a unique email ID. You may wish to change the email attached to the old username to a secondary email account (many use a free Yahoo email account for this purpose) so that your main email ID will be available for the new account.
c) In some cases, primarily when there is a legitimate security concern as in a case when a user has used their actual real name and now realizes that this was a poor decision for privacy or security reasons, one of the webmasters may be able to change the name on the user account. This is a very time-consuming process that puts a big hit on our database, as the change must be applied to every post they've made. This can only be done by WebmasterAlex during overnight maintenance. Because it is very time intensive, we will not do this for routine "I want a different name" requests. In these security-based instances, you must contact WebmasterAlex via PM or email, clearly explain the background and reason that you feel this is necessary, and provide the account name that you desire. When and whether he can accommodate the request will be at his discretion.
Hope this clears up the confusion.