I stumbled on the solution for this. In the file pluggable-functions.php in the wp-includes directory there are two lists at the beginning of the document. One is for the set_current_user function and the other is for get_current_user. I added the variables for the information I wanted to retrieve to each of these lists. Now I am able to get first name, last name and nickname in addition to the variables listed here.
This is the modified code:
if ( !function_exists('set_current_user') ) :
function set_current_user($id, $name = '') {
global $user_login, $userdata, $user_level, $user_fname, $user_lname, $user_nickname, $user_ID, $user_email, $user_url, $user_pass_md5, $user_identity, $current_user;
$current_user = '';
$current_user = new WP_User($id, $name);
$userdata = get_userdatabylogin($user_login);
$user_login = $userdata->user_login;
$user_level = $userdata->user_level;
$user_fname = $userdata->first_name;
$user_lname = $userdata->last_name;
$user_nickname = $userdata->nickname;
$user_ID = $userdata->ID;
$user_email = $userdata->user_email;
$user_url = $userdata->user_url;
$user_pass_md5 = md5($userdata->user_pass);
$user_identity = $userdata->display_name;
I had a feeling it would be easy! Hopefully this will help future customization freaks like me.