As of 2/4/15 you can now change your username, I'm sure most of you already know this though. What you need to know is this; if you change your username you will lose access to your inventory, enderchest, and money. As well as your claims but admins can recover those for you.
My main topic to talk about today though is how to find a players past username(s). If you go to http://mcuuid.net/ you can find the UUID of a person. We'll be using me as an example for all of this, my username is CritJ. So if you search for CritJ it will tell you my UUID is 34d56e4b-ce90-488e-8ec1-a65f973bbebf.
What you want to do from here copy and paste this URL into your browser https://api.mojang.com/user/profiles/(UUID)/names. You need to change the (UUID) in the URL to the players UUID. In my case this is 34d56e4b-ce90-488e-8ec1-a65f973bbebf, BUT, you need to remove the -'s. So the new UUID we want is 34d56e4bce90488e8ec1a65f973bbebf.
As a final result the URL is https://api.mojang.com/user/profiles/34d56e4bce90488e8ec1a65f973bbebf/names
If you need any help with this let me know. ~Crit