If you want to use a username that is already in use usurpation is the process by which you can get it. You can use this process to unify your account if the same username is used by different people on different wikis and one of them would like to use the same name in a unified manner on all wikis by requesting usurpation on the ones where he does not have control over his desired unified username. This is currently the only accepted reason for usurpation requests though this may change in the future.
For a rename request to an already existing account the following conditions need to be met:
the requester has been registered for at least 3 months at the time of request and has a cumulated edit count across all Wikimedia wikis of 400 or more;
the registered name of the requester is connected to the single user login system and he is the holder of the global account;
the requested new username is not connected to any non-deleted edits, except for edits on the user page and other edits that violate site policies (vandalism, copyright violation, etc.);
the holder of the requested new username is notified on his talk page and via e-mail (if she has enabled the option in their preferences), after which the user will be given a week to respond and choose a new name for herself;
where appropriate the bureaucrats, global renamers and stewards may deny a usurpation request that meets the above criteria;
renaming may not be possible due to technical and other constraints;
currently it is not possible to usurp a username from a user that has substantial edits, or to unify accounts where the global account is held by a different person, except where the holder of the chosen username consents to transfer the name.
The requests to change your username should be made at WP:RENAME.