I am being asked for an administrator name and password. To alllow my computer to update

If you own your own computer, when you first power it up when it is brand new, you are asked to create a local Username, and a password to go with it. If you are the first or only user on your computer, this will be the Admin username and password.

This Admin username and password are not related to any email names, web site names, or any Apple-ID names you may have. Because it is strictly local, this Admin name allows you to log in and make Major changes whether you are connected to the Internet or not.

This Admin name is the name being asked for in the dialog box you are showing. It is extremely unlikely to resemble what you typed in the box.

If you insist on it, AND you have a good internet connection, your Mac can allow the use of your Apple-ID as an emergency login ID.

But Apple-ID was never intended for software update, and does not work for installing software, and was only really intended as alternate logon for emergencies. Also if your internet connection is not good, the Apple-ID password can not be verified, so Apple-ID for login does not work AT ALL.

That (almost) looks like he might be confusing it with his Apple ID.