how can I do this with C# code?

This should obviously be a native feature of the XamChart

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

thanks, now it really looks nice.

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