Add options to Preferences: Backup, where the user can select to have Date and Time included in ALL backups, so that it is automatic when backing up. So the options shown in the image below are always checked
[Edited - Readability]
As you've shown, the option to append date and time is set on the Backup dialog. WHY would it need to be set in Preferences also?
If you open your backup folder, I expect you'll see that date and time are already present.