Na ten svoj kód zabudni a miesto neho daj tento:

Private Sub Worksheet_Change(ByVal Target As Range)
    On Error GoTo koniec
    Stlpec = WorksheetFunction.Match("Date", Rows("1:1"), 0)
    On Error GoTo 0
    If Target.Row <> 1 And Target.Column <> Stlpec Then
        Application.EnableEvents = False
        Cells(Target.Row, Stlpec) = Date
        Application.EnableEvents = True
    End If
    Exit Sub
koniec:
    MsgBox "Neexistuje stlpec so zahlavim ""Date""", vbExclamation, "Chyba"
End Sub