You must be talking about the iGoogle "random Pet of the Day" widget. The actual http://catoftheday.com home page only changes once a day. That little widget, though, was created by someone else, and picks animals at random from our archives, and refreshes each time you go to the page.

If you remember the cat's name, you can search for him by going to http://catoftheday.com - or clicking the kitty icon on the top of this page, same thing - and then hitting "search" on the buttons at the left.