One time username change from frontend?

Just add a meta record that tracks the state of the username-changing actions:

$user = wp_get_current_user();

$did_one_change = get_user_meta($user->ID, 'changed_username', true);

if($did_one_change !== false)
  wp_die('You already changed your user name once!');

wp_update_user(array(
  'ID'         => $user->ID, 
  'first_name' => $_POST['first_name'],
  'last_name'  => $_POST['last_name'],
));

// here add a meta entry that suggests the user has changed their name once
update_user_meta($user->ID, 'changed_username', 1);