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[...] recorded first by Snoopy4eva01 on 2009-03-05→ Steps to “Unsling” the NSLU2 [...]

require_once('/path/to/wp-config.php');
if (!is_user_logged_in()) auth_redirect(TRUE);
$wp_user_record = wp_get_current_user();
$username = $wp_user_record->user_login;

That is to say, I’ve done it by including WordPress’s functions and calling wp_get_current_user() to get the user record and go from there.

Given the username, there are certainly ways to go about extracting info from the database directly (which avoids the memory usage of loading up all of WP) and I think you can get the username from the cookies themselves (you’d have to have your scripts know about the WP cookie name stuff), but once you start tying into the system at that kind of lower level, the risk of major headaches on WP upgrades increases substantially.