Wpf – How to convert this TextBlock fade-in trigger to a Style

You can use a MultiBinding combined with the StringFormat property. Usage would resemble the following:

<TextBlock>
    <TextBlock.Text>    
        <MultiBinding StringFormat="{}{0} + {1}">
            <Binding Path="Name" />
            <Binding Path="ID" />
        </MultiBinding>
    </TextBlock.Text>
</TextBlock>

Giving Name a value of Foo and ID a value of 1, your output in the TextBlock would then be Foo + 1.

Note: that this is only supported in .NET 3.5 SP1 and 3.0 SP2 or later.

EDIT: I have overseen the fact that the TextBlock is in the ControlTemplate of your custom Window/Control. I do not think that it is possible to target a control within the ControlTemplate from a Storyboard outside of this ControlTemplate. You could however define a property on your custom Window which you then databind to your ChangeOccurred property, and then add the trigger to your ControlTemplate which will now get triggered by the custom Control's property rather than the Window's ViewModel's property (of course, indirectly it is triggered by the ViewModel because ChangeOccurred is bound to the property of the custom Window which in turn triggers the animation - uh, complex sentence, hope you understand). Is this an option? Could you follow? ;-)

Maybe some code helps:

public class MyCustomWindow : Window
{
    public static readonly DependencyProperty ChangeOccurred2 = DependencyProperty.Register(...);

    public bool ChangeOccurred2 { ... }

    // ...
}

And some XAML:

<local:MyCustomWindow ChangeOccurred2="{Binding ChangeOccurred}" ... >
    <!-- Your content here... -->
</local:MyCustomWindow>

<!-- Somewhere else (whereever your ControlTemplate is defined) -->
<ControlTemplate TargetType="{x:Type local:MyCustomWindow}">

    <!-- your template here -->

    <ControlTemplate.Triggers>
        <Trigger Property="ChangeOccurred2" Value="True">
            <Trigger.EnterActions>
                <BeginStoryboard>
                    <Storyboard BeginTime="00:00:00" Duration="0:0:2"
                                Storyboard.TargetName="txtWhatever"
                                Storyboard.TargetProperty="(Background).(SolidColorBrush.Color)">
                        <ColorAnimation FillBehavior="Stop"
                                        From="Black" To="Red"
                                        Duration="0:0:0.5"
                                        AutoReverse="True"/>
                    </Storyboard>
                </BeginStoryboard>
            </Trigger.EnterActions>
        </Trigger>
    </ControlTemplate.Triggers>
</ControlTemplate>

Note: I named the Window's property ChangeOccurred2 because I wanted it to be distinguishable from the ViewModel's ChangeOccurred property. Of course, you should choose a better name for this property. However, I am missing the background for such a decision.

My old answer:

So, you want to animate a TextBlock which is in the content of a (custom) Window?!

Why do you want to set the style on the Window, and not on the TextBlock itself? Maybe you should try something like this (did not test this!):

<local:MyCustomWindow ... >
    <!-- ... -->
    <TextBlock x:Name="textBlockAnimated" ... >
        <TextBlock.Style>
            <Style TargetType="{x:Type TextBlock}">
                <Style.Triggers>
                    <DataTrigger Binding="{Binding ChangeOccurred}" Value="True">
                        <DataTrigger.EnterActions>
                            <BeginStoryboard>
                                <Storyboard BeginTime="00:00:00" Duration="0:0:2"
                                            Storyboard.TargetProperty="(Background).(SolidColorBrush.Color)">
                                    <ColorAnimation FillBehavior="Stop"
                                                    From="Black" To="Red"
                                                    Duration="0:0:0.5"
                                                    AutoReverse="True"/>
                                </Storyboard>
                            </BeginStoryboard>
                        </DataTrigger.EnterActions>
                    </DataTrigger>
                </Style.Triggers>
            </Style>
        </TextBlock.Style>
    </TextBlock>
    <!-- ... -->
</local:MyCustomWindow>

The {Binding ChangeOccurred} might not be sufficient. You might have to add a DataContext to the TextBlock, or add a RelativeSource or something.