Here's one way, using a style on the ComboBox with triggers to set the ItemTemplate dynamically:
Edit: Changing the style into a resource. Note that this is still binding to the CheckBox directly using element binding - if you want it to be more flexible you could bind the CheckBox's IsChecked property to a property of your ViewModel and rely on that changing rather than IsChecked.
Let's move the style into the Resources section of our Window:
<Window.Resources>
<Style x:Key="myStyle" TargetType="ComboBox">
<Setter Property="ItemTemplate">
<Setter.Value>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding Name}" />
</StackPanel>
</DataTemplate>
</Setter.Value>
</Setter>
<Style.Triggers>
<DataTrigger Binding="{Binding IsChecked,ElementName=chk}" Value="True">
<Setter Property="ItemTemplate">
<Setter.Value>
<DataTemplate>
<StackPanel Orientation="Horizontal">
<TextBlock Text="{Binding ID}" />
<TextBlock Text=": " />
<TextBlock Text="{Binding Name}" />
</StackPanel>
</DataTemplate>
</Setter.Value>
</Setter>
</DataTrigger>
</Style.Triggers>
</Style>
</Window.Resources>
Now we define the CheckBox and a couple of ComboBoxes that rely on it:
<CheckBox x:Name="chk" Content="Click Me" />
<ComboBox ItemsSource="{Binding}" Style="{StaticResource myStyle}" />
<ComboBox ItemsSource="{Binding}" Style="{StaticResource myStyle}" />