You cannot have two changes in one action, as you don't changetwo cells in the same time,
but you can do an if condition in the following line which determine if the code should be executed or not,
for example:
Private Sub Worksheet_Change(ByVal Target As Range)
    Dim LRow&, lCol&
    If Not Intersect(Target, Columns(6)) Is Nothing Then
        If Cells(Target.Row, 15) = "Patrick" Then
            
            Range(Cells(Target.Row, 1), Cells(Target.Row, 17)).Copy  '<-- columns to be adjusted to your need
            LRow = Worksheets("Sheet2").Cells(Rows.Count, 1).End(xlUp).Row + 1
            Worksheets("Sheet2").Range("A" & LRow).PasteSpecial Paste:=xlPasteAll, Operation:=xlNone, SkipBlanks:=False, Transpose:=False
            lCol = Worksheets("Sheet2").Cells(LRow, Columns.Count).End(xlToLeft).Column
            Worksheets("Sheet2").Cells(LRow, lCol + 1) = Date
        Else
            'Do nothing or execute code to be placed here
        End If
    End If
End Sub
Cheers
Erwin