Hi! I'm in the process of emptying my account out and all I have left are the last of my pets that no one asked to adopt. Is the only way to do this to abandon them?

Er, yes? You go to the My Pets page and click 'Abandon Pet'. That will put it in the Adoption Agency.

You can just leave them where they are. After a year+ of being inactive your account will be erased from the system during a clearing what will make the names of your Pets become available again then as well. :)