It is possible to change the name of the hero in the "proper names" section of the hero, it is just below the very last number you see, which actually indicates how many names the hero "cycles" through.
Also you can make it so that when players type a message the name displayed is that of a particular pre desiganted name. An example would be when purple types the screen says "Tau: Hi guys" instead of "Malufa: Hi guys" if that makes sense.
No, it is not possible to my knowledge to go in and make the variables so that it would have the proper name of the hero that was chosen by the player as their "proper" name in the main text. It might be concievable with heavy JASS enscripting, but I doubt the result would be worth the effort.
I hope this helps clarify things for you, if not please indicate thus.