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.

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);
            }