loginout function customization

You might be looking for a logged in conditional. From the WP Codex, you might be able to try in your theme (untested):

<?php
if ( is_user_logged_in() ) {
    get_currentuserinfo();
    echo 'Logged in as ' . $current_user->user_firstname;
}
?>

EDIT

After consulting the WP Codex on the topic, I was able to display my user’s identity using the following:

if ( is_user_logged_in() ) {
    global $user_identity;
    get_currentuserinfo();  
    echo 'Logged in as ' . $user_identity;
}