You should do this in the ListPickerItemTemplate. Add Template to the page resources (or app resources)
<phone:PhoneApplicationPage.Resources>
<DataTemplate x:Name="ListPickerItemTemplate">
<StackPanel Orientation="Horizontal">
<TextBlock HorizontalAlignment="Right" Text="{Binding ItemName}"/>
</StackPanel>
</DataTemplate>
<DataTemplate x:Name="ListPickerFullModeItemTemplate">
<StackPanel Orientation="Horizontal">
<TextBlock HorizontalAlignment="Right" Text="{Binding ItemName}"/>
</StackPanel>
</DataTemplate>
</phone:PhoneApplicationPage.Resources>
and assign template to the picker:
<toolkit:ListPicker
ItemTemplate="{StaticResource ListPickerItemTemplate}"
FullModeItemTemplate="{StaticResource ListPickerFullModeItemTemplate}"
...