Name instance String variable after instance?

I want to give the variable name the name of the instances created.

For example: I create an instance of the Character-class and name that instance "teddy", now I want teddy.name to be "teddy". If I create an instance called "mandy" Debug.Log(mandy.name) should say "mandy".

How can I do that?

 public class Character
 {
         public var name : String; // = what do I need to assign it to?
         public var health : int;
         public var level : int;
 }
 
 static var teddy : Character = new Character();
 static var mandy : Character = new Character();

... also, is it possible the actual name to be "Teddy" starting with a big letter instead of "teddy". Maybe with an if-statement or something?

Thanks for reading my question! ;D