<UserControl x:Class="Testing.GameView"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  ...
  Focusable="True"
  x:Name="Root">
  	<Grid x:Name="RootGrid">
  	 	<local:MilestoneViewComponent 	PlayerData="{Binding PlayerData, Mode=OneWay, UpdateSourceTrigger=PropertyChanged}"
  	 					Money="{Binding CurrentMoney, Mode=OneWay, UpdateSourceTrigger=PropertyChanged}"/>
        </Grid>
</UserControl>

public partial class MilestoneViewComponent : UserControl, INotifyPropertyChanged {
	public event PropertyChangedEventHandler PropertyChanged;

	 public PlayerDataSO PlayerData {
    		get { return (PlayerDataSO) GetValue(PlayerDataProperty); }
    		set { SetValue(PlayerDataProperty, value); }
	}
	 public static void OnPlayerDataChanged(DependencyObject sender, DependencyPropertyChangedEventArgs e) {
     		MilestoneViewComponent milestoneViewComponent = sender as MilestoneViewComponent;
     		//Here some of my other bindings are updated that are read from the player
    		milestoneViewComponent.OnPropertyChanged(nameof(PlayerName));
    		/*
    			This is not getting called when I update the PlayerData
    		*/
 }
	 public static readonly DependencyProperty PlayerDataProperty = DependencyProperty.Register(
     		nameof(PlayerData), typeof(PlayerDataSO), typeof(MilestoneViewComponent), new PropertyMetadata(null, new PropertyChangedCallback(OnPlayerDataChanged)));
     	
     	public Float Money {
    		get { return (Float) GetValue(MoneyProperty); }
   		 set { SetValue(MoneyProperty, value); }
	}
	
	public static void OnMoneyChanged(DependencyObject sender, DependencyPropertyChangedEventArgs e) {
		MilestoneViewComponent milestoneViewComponent = sender as MilestoneViewComponent;
		//Here some of my other bindings are updated that are read from the player
    		milestoneViewComponent.OnPropertyChanged(nameof(PlayerName));
    		/*
    			This is getting called when I update Money
    		*/
	}
	public static readonly DependencyProperty MoneyProperty = DependencyProperty.Register(
   		 nameof(Money), typeof(Float), typeof(MilestoneViewComponent), new PropertyMetadata((Float) 0, new PropertyChangedCallback(OnMoneyChanged)));
     		
}	

<TextBlock Text="{Binding PlayerData.Name, ElementName=MilestoneView}"/>

<TextBlock Text="{Binding PlayerData.Name, ElementName=MilestoneView}"/>

public PlayerData PlayerData1; //dependency property
public PlayerData PlayerData2; //dependency property

//I'm calling a INotifyPropertyChanged within the UserControl to signal an update on this attribute
//when PlayerData inside my dependency properties have changed.
//This bool would be the value that actually get's displayed inside my UserControl
public bool HaveSameName {
	get { return PlayerData1.Name == PlayerData2.Name; }
}