Switching users in tic tac toe game

I am currently working on tic tac toe project with javascript html css.
The problem is I did set the constructors by the input of the user but
I cannot switch over the user when I play my game

My expectations are be able to switch user when you play your turn.
I tried if else by assigning currentplayer to player 1 if player 1 – I want to change it to player2

const gameBoard = (function() {
  // Select DOM elements
  const playerInput1 = document.querySelector("#player-select1");
  const playerButton = document.querySelector(".add-player");
  const playerInput2 = document.querySelector("#player-select2");
  const playerPara1 = document.querySelector(".player1");
  const playerPara2 = document.querySelector(".player2");
  const showPlayers = document.querySelector(".player-shows");
  const boxes = document.querySelectorAll(".box");

  // Game markers
  const gameMarker = ["O", "X"];
  let currentPlayer;
  let player1, player2;

  // Player factory function
  const playerSelection = (name, marker) => {
    let score = 0;
    return {
      name,
      marker,
      getScore: function() {
        return score;
      },
      scorePlus: function() {
        score++;
        return score;
      }
    };
  };

  // Initialize players
  player1 = playerSelection("Name", gameMarker[0]);
  player2 = playerSelection("Name", gameMarker[1]);

  // Event listener for player names
  playerButton.addEventListener("click", () => {
    player2.name = playerInput2.value.trim();
    player1.name = playerInput1.value.trim();

    if (player1.name === "" || player2.name === "") {
      alert("Please enter a name");
    } else {
      playerPara1.textContent = `First Player is: ${player1.name} (${player1.marker})`;
      playerPara2.textContent = `Second Player is: ${player2.name} (${player2.marker})`;
      showPlayers.innerHTML = "";
      showPlayers.append(playerPara1);
      showPlayers.append(playerPara2);

      // Start the game by setting the initial player
      playGame();
    }
  });

  // Add event listeners to boxes
  boxes.forEach((element) => {
    element.addEventListener("click", () => {
      if (element.textContent === "" && currentPlayer) { // Ensure box is empty and a player is set
        element.textContent = currentPlayer.marker; // Mark the box with the current player's marker
        playGame(); // Switch to the next player
      }
    });
  });

  // Function to switch current player
  const playGame = () => {
    if (currentPlayer === player1) {
      player1
    } else if (currentPlayer === player2) {
      player2
    }


  };

  // Return public methods
  return {
    playerSelection,
    playGame
  };
})();
<input type="text" id="player-select1">
<buttton class="add-player">Add</button>
<input type="text" id="player-select2">
<p class="player1"></p>
<p class="player2"></p>

<div class="player-shows"></div>

<div id="board">
<div class="box"></div>
<div class="box"></div>
<div class="box"></div>
<br>
<div class="box"></div>
<div class="box"></div>
<div class="box"></div>
<br>
<div class="box"></div>
<div class="box"></div>
<div class="box"></div>
<br>
</div>