Add Name
property to your Label
<Label x:Name="myLabel" Content="" HorizontalAlignment="Left" Margin="10,64,0,0" VerticalAlignment="Top" Width="497"/>
So you can access it here
protected override void OnStartup(StartupEventArgs e)
{
base.OnStartup(e);
MainWindow mainWindow = new MainWindow();
mainWindow.Show();
//Change the label in MainWindow
mainWindow.myLabel.Content = "Hello World";
}