Unable to verify account name or password. It's not going to close. How can I fix this?

Shut down or restart your Mac - Apple Support

"You can force a shutdown if necessary—for example, if your Mac becomes unresponsive—by pressing and holding the power button until your Mac shuts down. You may lose unsaved changes in open documents."

You say you recently purchased this computer. Was that brand new from Apple, or was it from somebody else? Is it possible it had a previous owner?

Have you tried clicking "OK"?

If you're asking about the sign in issue, we need more context. You apparently neither have the user name nor the password for the account. Are you the owner of the computer?