The code doesn't identify which row the match is found in. If there is only one line that will have matching Name/Places, this line should remove the matching row.
[VBA]Sheets("Sheet2").Cells(Evaluate("SUMPRODUCT(--(Sheet2!$A$1:$A$100=" & Chr(34) & uiName & Chr(34) _
& "),(--(Sheet2!$B$1:$B$100=" & Chr(34) & uiPlace & Chr(34) & ")),ROW(Sheet2!$A$1:$A$100))"),1).EntireRow.Delete[/VBA]