When authenticated using basic or digest authentication in apache, the username is stored in the http header REMOTE_USER. If you are using php, the username and password are also stored in the http header as PHP_AUTH_USER and PHP_AUTH_PW.
Regarding logout, cPanel has a logout link. It works as dmadance requires. I dont know if cPanel simply deletes the value for REMOTE_USER or something else entirely. But I use it all the time to switch between various remote databases managed with PHPmyAdmin.