Unable to make system changes on MacBook Air after changing administrator name

Here are the instructions that @WheelieNick mentioned:

Try booting into Single User Mode using Command + S.

Follow the instructions listed on screen to run a file system check and mount the file system in read+write mode. I'm reproducing the commands here from memory:

fsck  -fy  /
mount  -uw  /

Then issue the following command:

rm  -i  /var/db/.AppleSetupDone

You will be prompted to confirm you want to delete the ".AppleSetupDone" file. If you are sure you are deleting the correct file then press "y" followed by pressing the "Return" key to submit your response. Otherwise press "n" followed by the "Return" key to cancel the deletion of the listed item.

Now type:

reboot

to restart the Mac. By deleting the ".AppleSetupDone" file it will trick macOS to run Setup Assistant on the next system boot where you will be able to create a new admin user account. Once you create and log into the new admin user account you can fix the mistake by using the instructions in the following Apple article as a guide:

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

To fix this issue, you must create a temporary administrator account by running the setup assistant again via Single User Mode, and then use that new account to repair or properly re-link your original account.