Add the ability to set the player names

Somewhere near the top of HaveTurn, while you're declaring variables, you'll want to add the following code:

// something here...
            Console.WriteLine("Player One, input your name:");
            string PlayerOneName = Convert.ToString(Console.ReadLine());
            Console.WriteLine("Player Two, input you name:");
            string PlayerTwoName = Convert.ToString(Console.ReadLine());
// something here...

Lower down, there's a while loop that looks like this:

while (PlayerOneTilesPlayed <= MaxTilesPlayed && PlayerTwoTilesPlayed <= MaxTilesPlayed && PlayerOneTiles.Length < MaxHandSize && PlayerTwoTiles.Length < MaxHandSize)
            {
                HaveTurn("Player One", ref PlayerOneTiles, ref PlayerOneTilesPlayed, ref PlayerOneScore, TileDictionary, ref TileQueue, AllowedWords, MaxHandSize, NoOfEndOfTurnTiles);
                Console.WriteLine();
                Console.WriteLine("Press Enter to continue");
                Console.ReadLine();
                Console.WriteLine();
                HaveTurn("Player Two", ref PlayerTwoTiles, ref PlayerTwoTilesPlayed, ref PlayerTwoScore, TileDictionary, ref TileQueue, AllowedWords, MaxHandSize, NoOfEndOfTurnTiles);
            }

Just swap "Player One" and "Player Two" with your variables for the player's names, like so:

while (PlayerOneTilesPlayed <= MaxTilesPlayed && PlayerTwoTilesPlayed <= MaxTilesPlayed && PlayerOneTiles.Length < MaxHandSize && PlayerTwoTiles.Length < MaxHandSize)
            {
                HaveTurn(PlayerOneName, ref PlayerOneTiles, ref PlayerOneTilesPlayed, ref PlayerOneScore, TileDictionary, ref TileQueue, AllowedWords, MaxHandSize, NoOfEndOfTurnTiles);
                Console.WriteLine();
                Console.WriteLine("Press Enter to continue");
                Console.ReadLine();
                Console.WriteLine();
                HaveTurn(PlayerTwoName, ref PlayerTwoTiles, ref PlayerTwoTilesPlayed, ref PlayerTwoScore, TileDictionary, ref TileQueue, AllowedWords, MaxHandSize, NoOfEndOfTurnTiles);
            }

A few changes also need to be made to DisplayWinner.

private static void DisplayWinner(int PlayerOneScore, int PlayerTwoScore, string PlayerOneName, string PlayerTwoName)
        {
            Console.WriteLine();
            Console.WriteLine("**** GAME OVER! ****");
            Console.WriteLine();
            Console.WriteLine(PlayerOneName + ", your score is " + PlayerOneScore);
            Console.WriteLine(PlayerTwoName + ", your score is " + PlayerTwoScore);
            if (PlayerOneScore > PlayerTwoScore)
            {
                Console.WriteLine(PlayerOneName + " wins!");
            }
            else if (PlayerTwoScore > PlayerOneScore)
            {
                Console.WriteLine(PlayerTwoName + " wins!");
            }
            else
            {
                Console.WriteLine("It is a draw!");
            }
            Console.WriteLine();
        }

When DisplayWinner is called from HaveTurn, make sure to pass it the new variables:

DisplayWinner(PlayerOneScore, PlayerTwoScore, PlayerOneName, PlayerTwoName);