How could you change the name of the player's character without using the race menu?

I tried :

Game.GetPlayer().GetBaseObject().SetName("Sam")

and saw that it can't be used on actors or object references - only form

http://www.creationkit.com/SetName_-_Form

How is this done?

The code you've posted is exactly what's renaming the player to Sam. Actor Base is a Form. So, as long as you get the base actor or object, you can rename everything that has a name tag inside their properties. That'd be actors, activators, items, floras etc. etc. etc.