The Apple ID is only used to verify the licence during installation and isn't stored after that.
The best way to "tidy up" a fresh installation is convoluted because you can't delete the last remaining user from inside the GUI. You don't absolutely have to do this, but if you want the system to boot to the original Setup Assistant then here's how you do it:
Edit: Step 0: Deauthorise your iTunes account if you haven't already! It's done by hardware serial number so you can still do this after reformatting if you forgot about it.
1. Boot into single-user mode by holding Cmd-S at the chime. 2. When prompted, type "/sbin/fsck -fy" and "/sbin/mount -uw /" as requested. 3. Type the following commands.