So far it seems no one has suggested a scheme for noting which color was stalemated White or Black. Obviously the player who can't move is the one stalemated but how would you note that result on a database or say a result sheet where the game score isn't available?
There is zero need to note such things. A draw is a draw and a win is a win, how the status was reached is totally irrelevant unless you are interested in the game, and then you don't need the notation anyway.

You know which side did the stalemating by seeing who made the last move.