Rename User

I recently purchases a used mac. It has the old user name all over it and I can't figure out how to change it. I changed the admin to myself but the users didn't change, nor did the settings such as the name when the password box pops up. I can see a different name as a folder name (not person's full name as I keep seeing) under user and I tried to change that but it's locked.

Thank you in advance.

 

I created a new user, and deleted the old one. nothing. I don't want to reinstall because then I have to reinstall all the programs the user before me has. I don't have the discs and I'd like the programs that came with computer.

 

If I am in the right place it is System > accounts. I changed the admin to myself, but when you go to finder and you see the little house, it's still old user name. It's kinda a crappy name so I'd rather not look at it everyday