I accidentally renamed my administrator's account and now I cannot unlock system preferences. How can I fix this situation?

if you have tried old name and new name.

correct process is Change the name of your macOS user account and home folder - Apple Support

if you are not able to unlock follow below for a completely new account.. make the correct changes to your primary account..test it, then remove the new one you made

You can create a new administrator account by restarting the Setup Assistant:

1. Boot into Single User Mode: Start/restart your Mac. As soon as you hear the startup tone, press and hold ⌘ + S until you see a black screen with white lettering. (If you end up back on the login screen after a flash of the black screen with white lettering, enter your password and it will return to the black screen.)
2. Check and repair the drive by typing

   /sbin/fsck -fy

   then ↩ enter - as directed by the on-screen text.
3. Mount the drive as read-write by typing

   /sbin/mount -uw /

   then ↩ enter.
4. Remove the Apple Setup Done file by typing

   rm /var/db/.AppleSetupDone

   then ↩ enter.
5. Reboot by typing

   reboot

   then ↩ enter.
6. Complete the setup process, creating a new admin account.