All objects in array are equal to last added object c#

I have created a class named "Player" which stores data for each player. The class does what it should do, but when storing multiple instances of the class in a List/Array, all objects in the array or list are equal to the last stored object.

Player class code:

public class Player
{
    private static string player_name;
    public Player(string name)
    {
        player_name = name;
    }
    public string Name
    {
        get
        {
            return player_name;
        }
    }
}

code for creating and adding to the list:

//simple string array for names;
string[] example_names = new string[] { "Mike", "Adam", "Jake" };

//creating new object and adding to list<Player>
List<Player> players = new List<Player>();
foreach (string name in example_names)
{
     Player player = new Player(name);
     players.Add(player);
}

//loop for returning the output
string output = "";
foreach (Player player in players)
{
    output += player.Name + ", ";
}
Clipboard.SetText(output);

output: "Jake, Jake, Jake, "