In my wife's account iCloud keeps popping in a message asking for the password. However, iCloud is using a user name from an obsolete account. This is a new issue as iCloud has been using the username from when we updated all the information a few months ago.

How do I get iCloud to use the user name that was provided when we updated the information?

Check in System Preferences>iCloud to see which account name is in use. Even if it is the correct one, sign out and sign back in with the updated info. See if this will banish the old account info request.

Check any iDevices to verify that their iCloud account is the one you want, too.

Look also in Safari > Preferences > Passwords.