Go to: http://www.thesecretworld.com/
click on: My Account and choose "The Secret World Account"
on the left, click on: Game-> Change My Password
on the dropdown menu that says "Billing and All Game Passwords" change to "Game Password"
Put in your desired password
You might have to wait a cpl of minutes or maybe close and relaunch client again before trying again
you should now be able to log in