Game states

A simple way to get started with different states in the game is to use a simple state machine. Declare an enum with the different game states.

enum GameState
{
    MainMenu,
    Gameplay,
    EndOfGame,
}

In your Game class, declare a member of the GameState type.

GameState state = GameState.MainMenu;

In your Update() method, use the _state to determine which update to run.

void Update(GameTime gameTime)
{
    base.Update(gameTime);
    switch (state)
    {
    case GameState.MainMenu:
        UpdateMainMenu(gameTime);
        break;
    case GameState.Gameplay:
        UpdateGameplay(gameTime);
        break;
    case GameState.EndOfGame:
        UpdateEndOfGame(gameTime);
        break;
    }
}

Now define the UpdateMainmenu(), UpdateGameplay() and UpdateEndOfGame().

void UpdateMainMenu(GameTime gameTime)
{
    // Respond to user input for menu selections, etc
    if (pushedStartGameButton)
        state = GameState.GamePlay;
}

void UpdateGameplay(GameTime gameTime)
{
    // Respond to user actions in the game.
    // Update enemies
    // Handle collisions
    if (playerDied)
        state = GameState.EndOfGame;
}

void UpdateEndOfGame(GameTime gameTime)
{
    // Update scores
    // Do any animations, effects, etc for getting a high score
    // Respond to user input to restart level, or go back to main menu
    if (pushedMainMenuButton)
        state = GameState.MainMenu;
    else if (pushedRestartLevelButton)
    {
        ResetLevel();
        state = GameState.Gameplay;
    }
}

In the Game.Draw() method, again handle the different game states.

void Draw(GameTime gameTime)
{
    base.Draw(gameTime);
    switch (state)
    {
    case GameState.MainMenu:
        DrawMainMenu(gameTime);
        break;
    case GameState.Gameplay:
        DrawGameplay(gameTime);
        break;
    case GameState.EndOfGame:
        DrawEndOfGame(gameTime);
        break;
    }
}

Now define the different Draw methods.

void DrawMainMenu(GameTime gameTime)
{
    // Draw the main menu, any active selections, etc
}

void DrawGameplay(GameTime gameTime)
{
    // Draw the background the level
    // Draw enemies
    // Draw the player
}

void DrawEndOfGame(GameTime gameTime)
{
    // Draw text and scores
    // Draw menu for restarting level or going back to main menu
}

OnChange event on enum

You could use a private variable, but have a public property. Within the set of the property you could run a method which will be run every time use change the enum value with the property:

public enum PersonName
  {
      Eric,
      George,
      David,
      Frank
  }

  private PersonName myPersonName

  public PersonName MyPersonName
  {
      get { return myPersonName; }
      set
      {
          myPersonName = value;
          //simply call what you want done
          PersonNamePropertyChanged();
      }
  }