Mojave insists on a non-existent login & password

From the kb above:

If you still can't log in

If you still can't log in with your password, contact Apple Support for help.

or you can take in for help:

In or out of warranty you can get a free over the counter 'Apple Service Diagnostics' test and Assessment

https://www.apple.com/retail/geniusbar/

https://checkcoverage.apple.com/

https://support.apple.com/my-support

https://support.apple.com/en-lamr/aasp-program

From iOS online Genius Bar appointment:

https://itunes.apple.com/us/app/apple-support/id1130498044?mt=8

Northwind58 wrote:

I upgraded my late 2012 iMac, and now it sits there wanting me to sign in with user name and password. Problem is, ghis is a private computer and I don’t have a user name or password.

What do mean, you have no user name or password, how can this be?

Your admin account has a username and a password. What is the problem. Is this your computer?

Northwind58 wrote:

Of course this is my Mac. The whole family uses it so I did not set it up to be password protected. I’m anal about making notes of my dozens of logins, and I have nothing for this Mac. If I did set one up it would have been my standby, which doesn’t work. And there’s no “forgot my password” link. I’m not the only one going through this, others have posted about this same issue.

Reset your Mac login password - Apple Support

If you setup Filevault while installing Mojave then it is looking for a FileVault password. You can verify this by looking at  > System Preferences> Security & Privacy ref:

Use FileVault to encrypt the startup disk on your Mac - Apple Support