In order to post as a character, you will need to create a character on the site you're a member of. This can be done on the Roster of the site or on your User Profile.
Once you've done this, go to the Sites tab of your User Profile and scroll down until you find the site you'd like to set this for. There will be an option for Settings. Click that link, select the character you would like to post as from the dropdown menu, then click the 'Set Character to Post As' button and you're set!
Please note that this feature does not hide your actual account name - it will still appear below the character's name, to avoid confusion.