Get current custom user taxonomy

Try this suggestion:

$user_id = get_current_user_id();  // Get current user Id
$user_groups = wp_get_object_terms($user_id, 'user-group', array('fields' => 'all_with_object_id'));  // Get user group detail
foreach($user_groups as $user_gro)
{
    echo $user_gro->name; // Get current user group name
    echo $user_gro->taxonomy; // get current user taxonomy 
}