Can't change my administrator name

Yes.

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.

Be very careful to notice the spaces in those Terminal Commands.

Once you've done that the computer reboots and it's like the first time you used the machine. Your old accounts are all safe. From there you just change all other account passwords in the account preferences!!

Also, when in Users and Groups, where my user is listed, it states "Standard" not Admin as on my Macbook Pro...

Does this have any affect as it's a standard user and not the administrator??

Yes, but there isn't any "the administrator" on Unix and macOS. Users can be marked in a way that allows them to elevate their privileges through authentication, when needed. Any user can have this power, so there isn't a single administrator account on macOS.

The first account created on the system is given the ability to administrate the computer. I don't know other ways to lose that capability, but the most common here is trying to change the short user name of the account while logged into that same account.

BDAqua has provided the steps to have the system create a new user that has admin privileges.

Can you create a new admin user?

Did you attempt to change the username before this? Doing so from that user account will strip its admin capability.