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.

launchctl load /System/Library/LaunchDaemons/com.apple.opendirectoryd.plist
dscl . -list /groups GroupMembership | grep Mac

You may get an error (which can be ignored) but should get a list of groups that the user "Mac" is a member of.

4. Remove the user from each group by typing this command for each group:

dscl . delete /groups/GROUPNAME GroupMembership Mac (you may get another error which can be ignored)

5. Clean up the user account:

dscl . delete /groups/Mac (this one may not exist)
dscl . delete /users/Mac
rm /private/var/db/dslocal/nodes/Default/users/Mac.plist (this may also not exist)
rm -rf /Users/Mac

6. Finally, restore the Setup Assistant and reboot:

rm /private/var/db/.AppleSetupDone
reboot

7. Once the system comes back up, it should boot into the Setup Assistant. Press Cmd-Q and select to shut down. It'll continue to boot into the Assistant, just like a brand-new machine :)