How to solve disturbance in my bot in c#?

As @Andy Lamb wrote in a comment, your problem is that you are managing only one “game”, so every player interacts with each other.

You must find a way to identify the sender of each message, and manage a “game” for each player.

A game object should be an instance of a class, maintaining all the data which is linked to a single player game (e.g. desired_word, etc). Your while (true) loop should look something like this:

while (true) {
  var  updates = await bot.MakeRequestAsync(new GetUpdates() { Offset = offset });
  foreach(var update in updates) {
    var sender = GetSender(update);
    var game = RetrieveGameOrInit(sender);

    // ... rest of your processing, but your code is a little messy and
    // you have to figure out how to refactor the processing by yourself
    game.Update(update);

    // do something with game, and possibly remove it if it's over.
  }
}


public string GetSender(UpdateResponseOrSomething update)
{
    // use the Telegram API to find a key to uniquely identify the sender of the message.
    // the string returned should be the unique identifier and it
    // could be an instance of another type, depending upon Telegram
    // API implementation: e.g. an int, or a Guid.
}

private Dictionary<string, Game> _runningGamesCache = new Dictionary<string, Game>();

public Game RetrieveGameOrInit(string senderId)
{
    if (!_runningGamesCache.ContainsKey(senderId))
    {
       _runningGamesCache[senderId] = InitGameForSender(senderId);
    }

    return _runningGamesCache[senderId];
}

/// Game.cs
public class Game
{
  public string SenderId { get; set; }
  public string DesiredWord { get; set; }
  // ... etc

  public void Update(UpdateResponseOrSomething update)
  {
    // manage the update of the game, as in your code.
  }
}

Hope it helps!