If your operator is logging into a windows domain on the computer with the internet explorer they're using to view ssrs reports, you can make use of the "built in field" UserID. I used this built in field as the default value for a parameter and send it over via reporting services. However its worth mentioning that you can also specify parameters to SSRS manually via the URL so in a sense SSRS will be trusting the browser to tell it who the user is, and this will allow a hole for impersonation (security problem).
To demonstrate the unsecure method, I create a report that has a report parameter called ReportParameter1, that I set to have a default value in the expression builder as: =User!UserID and this value will be the username of who is running the browser. But I could spoof the user simply by building a url with the report parameter built in like so:
but I use it as the username is more for informational purposes and I'm not using it to expose sensitive info as whoever can run the report is already authorized to view the data so it works for my use case. It is in reality no security at all, just usable for information.
Apologies if this isn't what you were talking about.