Until someone provides the answer for how to accomplish your task automatically, you may have to resort to some manual methods that could be supplemented by Draconian enforcement steps.
By this I mean the following:
1. The "manual" method: Create an internal department or company policy that requires anyone who creates (or modifies or runs) an NCM Policy Report (especially one that has a Compliance remediation script active within it) must modify the report's Name or Description to include their User Name before they run it. The Description can contain anything you wish, but it should always include information about the intent of the Report, the changes recently applied, and especially any Remediation that is applied within the Rules that the Report/Policy references.
2. The "Draconian" enforcement: Your internal corporate policy regarding NCM reports that perform Remediation should have consequences for those who do not follow that policy. If someone does not modify the report with their name, and then runs it and causes changes on the network via the Remediation scripting, their access to NCM is removed. They can't make that mistake again.
Reports with Remediation scripts are incredibly powerful and mindless. They're good examples of computers doing exactly what you tell them to do. If users inadvertently (or intentionally) harm the network through these reports and remediation scripts, they have no business managing NCM.
It's not far from driving a care and intentionally or careless hitting a mail box or a pedestrian. Your driving privileges can be revoked, as can NCM privileges if someone doesn't follow the rules to update the scheduled report to include their name on it.
Yes, this is sadly manual. Yes, the enforcement is unfriendly. Yes, SW should have an option to automatically list who ran the report every time. And maybe it exists--maybe someone knows how to do this. jiri.cermak might be a good resource for this--if he doesn't know if this can be done, and how to do it, I bet he knows someone that does.
This is a great opportunity for you to create a new Feature Request, if someone doesn't know how to accomplish what you want. Just go to the Thwack community page and look for the top right area that says "Create." Use its drop down and select "New Feature Request" and put in exactly what you'd like.
Folks will vote on it, maybe a future version of NCM will have just what you asked for.
Thanks for the advice. Off to ask for a New Feature