Each mapping writes its filter into the chosen parameter when Apply is pressed. Set these up first: the table SQL below reads each parameter as <Parameters.Name>, splitting the value as the SQL template below shows.
Custom parameters
Each row writes a typed value, or the value another parameter holds, into the chosen parameter when Apply is pressed, before the load reads it.
SQL template
Table
Create a calculated field USERNAME(), create a string parameter, set its "Value when workbook opens" to that field, then pick the parameter here. Do not place the parameter control on the dashboard: viewers can change it. Every viewer loads rows under the name it holds.
Set up both: the custom SQL decides what is shown, and the data source filter guarantees a viewer can never see another viewer's rows even if the parameter is changed.