how can I do this with C# code?

Here's an example of how you can make the axis titles more dynamic, through the use of attached properties:

The Xaml:

<Window.Resources>
        <ControlTemplate x:Key="chartTemplate" TargetType="igChart:XamChart">
            <Grid>
                <Grid.ColumnDefinitions>
                    <ColumnDefinition Width="Auto" />
                    <ColumnDefinition />
                </Grid.ColumnDefinitions>
                <Grid.RowDefinitions>
                    <RowDefinition />
                    <RowDefinition Height="Auto" />
                </Grid.RowDefinitions>
                <ContentPresenter Name="PART_Default_Chart" 
                                  Grid.Row="0" Grid.Column="1" />
                <TextBlock Grid.Row="0" Grid.RowSpan="2" 
                           Grid.Column="0" TextAlignment="Center"
                           Text="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=(local:AxisInfo.YAxisTitle)}">
                    <TextBlock.LayoutTransform>
                        <RotateTransform Angle="90" />
                    </TextBlock.LayoutTransform>
                </TextBlock>
                <TextBlock Grid.Row="1" Grid.ColumnSpan="2" 
                           Text="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=(local:AxisInfo.XAxisTitle)}"
                           TextAlignment="Center" />
            </Grid>
        </ControlTemplate>
    </Window.Resources>
    <Grid>
        <Grid.RowDefinitions>
            <RowDefinition />
            <RowDefinition Height="Auto"/>
        </Grid.RowDefinitions>
        
        <igChart:XamChart x:Name="theChart" 
                          Template="{StaticResource chartTemplate}"
                          local:AxisInfo.XAxisTitle="XAxis"
                          local:AxisInfo.YAxisTitle="YAxis">
        </igChart:XamChart>
        
        <Button x:Name="changeTitles" 
                Content="Change Titles" 
                Click="changeTitles_Click"
                Grid.Row="1"/>
    </Grid>

And the code behind:

    public partial class MainWindow : Window
    {
        public MainWindow()
        {
            InitializeComponent();
        }

        private void changeTitles_Click(object sender, RoutedEventArgs e)
        {
            AxisInfo.SetXAxisTitle(theChart, "Another X title");
            AxisInfo.SetYAxisTitle(theChart, "Another Y title");
        }
    }

    public static class AxisInfo
    {
        public static readonly DependencyProperty XAxisTitleProperty =
            DependencyProperty.RegisterAttached(
            "XAxisTitle",
            typeof(string),
            typeof(AxisInfo),
            new PropertyMetadata("X Axis"));

        public static string GetXAxisTitle(
            DependencyObject target)
        {
            return (string)target.GetValue(XAxisTitleProperty);
        }

        public static void SetXAxisTitle(
            DependencyObject target, 
            string title)
        {
            target.SetValue(XAxisTitleProperty, title);
        }

        public static readonly DependencyProperty YAxisTitleProperty =
            DependencyProperty.RegisterAttached(
            "YAxisTitle",
            typeof(string),
            typeof(AxisInfo),
            new PropertyMetadata("Y Axis"));

        public static string GetYAxisTitle(
            DependencyObject target)
        {
            return (string)target.GetValue(YAxisTitleProperty);
        }

        public static void SetYAxisTitle(
            DependencyObject target,
            string title)
        {
            target.SetValue(YAxisTitleProperty, title);
        }
    }

When I change the theme, it seems to work. The axis labels aren't effected by the change, because they are just in the static template that we are setting. Changing the theme works by changing the control templates of the Infragistics controls. But you are setting a template manually that has a static text styling on the labels. You may have to make multiple versions of this template and swap them as the theme changes to make the axis labels style change appropriately along with the theme.

for 3. I see the caption in this example, do you?

-Graham

When you set the chart's template the theme change is not allowed to override the chart's template, so some details of the neon theme at the level of the chart are lost. You can adjust for this by reconciling the template you are specifying with the neon theme's template. Here's the modified version:

<Window.Resources>
        <SolidColorBrush x:Key="CaptionForegroundBrush" Color="#FFFFFFFF"/>
        <Style x:Key="captionStyle" TargetType="TextBlock">
            <Setter Property="Foreground" Value="{StaticResource CaptionForegroundBrush}"/>
            <Setter Property="FontFamily" Value="/xamFeatureBrowserResources;Component/fonts/#Avenir"/>
            <Setter Property="FontSize" Value="16"/>
            <Setter Property="FontWeight" Value="Bold" />
        </Style>
        <ControlTemplate x:Key="chartTemplate" TargetType="igChart:XamChart">
            <Border 
                Background="{TemplateBinding Background}" 
                BorderBrush="{TemplateBinding BorderBrush}" 
                BorderThickness="{TemplateBinding BorderThickness}" 
                CornerRadius="0,0,0,0">
            <Grid >
                <Grid.ColumnDefinitions>
                    <ColumnDefinition Width="Auto" />
                    <ColumnDefinition />
                </Grid.ColumnDefinitions>
                <Grid.RowDefinitions>
                    <RowDefinition />
                    <RowDefinition Height="Auto" />
                </Grid.RowDefinitions>
                <ContentPresenter Name="PART_Default_Chart" 
                                  Grid.Row="0" Grid.Column="1" />
                <TextBlock Grid.Row="0" Grid.RowSpan="2" 
                           Grid.Column="0" TextAlignment="Center"
                           Style="{StaticResource captionStyle}"
                           Text="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=(local:AxisInfo.YAxisTitle)}">
                    <TextBlock.LayoutTransform>
                        <RotateTransform Angle="90" />
                    </TextBlock.LayoutTransform>
                </TextBlock>
                <TextBlock Grid.Row="1" Grid.ColumnSpan="2" 
                           Style="{StaticResource captionStyle}"
                           Text="{Binding RelativeSource={RelativeSource TemplatedParent}, Path=(local:AxisInfo.XAxisTitle)}"
                           TextAlignment="Center" />
            </Grid>
            </Border>
        </ControlTemplate>
    </Window.Resources>

Hope this helps!

-Graham

thanks, now it really looks nice.

Why aren't such labels provided in the xamchart?  A caption is provided, why not these labels?

This should obviously be a native feature of the XamChart