How to update path of a page

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Let's say I have a page that has as name of
cats
and a handle of
cats
. Currently, the page is accessible viahttp://whatever.com/cats

Now, I want to update the URL for that page.

<?php
$page = Page::getById(123);
$page->update(array('cname'=>'cats2', 'cHandle'=>'cats2'));


The page name is updated, and it appears the handle is updated as well, but I can still only access the page viahttp://whatever.com/cats

I want to be able to access the page viahttp://whatever.com/cats2

How can I make this possible?