Welcome!
The available Power BI actions are
quite limited currently, and the
triggers are too, meaning that as far as I know of there's no way to do exactly what you want. Does the report get published regularly? If so, you could set your flow to run on a regular schedule based on when you know the report will be refreshed and then export the PBI report and add it as an attachment to an email.
I do not think there is any way to actually read the data of a report and include it as parameters for a flow, so you might be stuck doing that manually. I do know there is a thing in PBI called data driven alerts (
Set data alerts in the Power BI service - Power BI), but I believe they have to be on a dashboard, not a report.
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So another thought. Where does your data come from? Depending on where it comes from and what kind of analysis is done to create the table with names, it might be possible to get what you want by creating a flow connected straight to the data source.