Customizing backup filenames

Problem/Motivation

Backup settings have config for the database and public/private files.
The filename is configured in the backup settings.
You could use one setting for all your scheduled backups, but they will have the same filename.
This is confusing because the full backup is not supported and individual db/file backups should be scheduled.
You can create multiple backup settings to set different names, but this is tedious and redundant.
The name can't be customized beyond a static string and datetime settings.

Proposed resolution

Allow setting a filename override in the schedule settings.
Allow using tokens in the filename.

Remaining tasks

Discuss proposal and implement solution.