Jay,
In C#, unless the class is static, classes without constructors are given a public default constructor by the C# compiler in order to enable class instantiation.
So, although your class does not have a constructor, you can still instantiate it.
For example: Player myPlayer = new Player();
.
Back to your case, you can declare a variable of type Player in your Form class and instantiate it as the above example, or just declare the variable and instantiate it in the Form's constructor, or Load event.
In the event handler for the button click, you then set the name of the Player instance.
myPlayer.Name = Pname.Text;
It depends on what you need, but I think newing the Player every time the button is clicked is kind of wasteful.