For the sake of argument, here's a simple person class

public class Person : DependencyObject, INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;

    public static readonly DependencyProperty FirstNameProperty =
        DependencyProperty.Register( "FirstName",
                                     typeof ( string ),
                                     typeof ( Person ),
                                     null );
    public static readonly DependencyProperty LastNameProperty =
        DependencyProperty.Register( "LastName",
                                     typeof( string ),
                                     typeof( Person ),
                                     null );

    public string FirstName
    {
        get
        {
            return ( string ) GetValue( FirstNameProperty );
        }
        set
        {
            SetValue( FirstNameProperty, value );
            if(PropertyChanged != null)
                PropertyChanged(this, new PropertyChangedEventArgs( "FirstName" ));
        }
    }

    public string LastName
    {
        get
        {
            return ( string ) GetValue( LastNameProperty );
        }
        set
        {
            SetValue( LastNameProperty, value );
            if ( PropertyChanged != null )
                PropertyChanged( this, new PropertyChangedEventArgs( "LastName" ) );
        }
    }
}

I want to go about creating a readonly property like this

public string FullName
    {
        get { return FirstName + " " + LastName; }
    }

How does binding work in this scenario? I've tried adding a DependancyProperty and raised the PropertyChanged event for the fullname. Basically I just want to have a property that I can bind to that returns the fullname of a user whenever the first or last name changes. Here's the final class I'm using with the modifications.

public class Person : DependencyObject, INotifyPropertyChanged
{
    public event PropertyChangedEventHandler PropertyChanged;

    public static readonly DependencyProperty FirstNameProperty =
        DependencyProperty.Register( "FirstName",
                                     typeof ( string ),
                                     typeof ( Person ),
                                     null );
    public static readonly DependencyProperty LastNameProperty =
        DependencyProperty.Register( "LastName",
                                     typeof( string ),
                                     typeof( Person ),
                                     null );
    public static readonly DependencyProperty FullNameProperty =
        DependencyProperty.Register( "FullName",
                                     typeof( string ),
                                     typeof( Person ),
                                     null );

    public string FirstName
    {
        get
        {
            return ( string ) GetValue( FirstNameProperty );
        }
        set
        {
            SetValue( FirstNameProperty, value );
            if ( PropertyChanged != null )
            {
                PropertyChanged( this, new PropertyChangedEventArgs( "FirstName" ) );
                PropertyChanged( this, new PropertyChangedEventArgs( "FullName" ) );
            }
        }
    }

    public string LastName
    {
        get
        {
            return ( string ) GetValue( LastNameProperty );
        }
        set
        {
            SetValue( LastNameProperty, value );
            if ( PropertyChanged != null )
            {
                PropertyChanged( this, new PropertyChangedEventArgs( "LastName" ) );
                PropertyChanged( this, new PropertyChangedEventArgs( "FullName" ) );
            }
        }
    }

    public string FullName
    {
        get { return GetValue( FirstNameProperty ) + " " + GetValue( LastNameProperty ); }
    }
}