Well, seeing as my name is Graham, and its often shortened to Grey or Gray, I've no idea which. My wife doesn't know either she writes on or the other on cards. I've even had Gray on the envelope and Grey in the card!
I've actually never heard of Gray/Grey being a nickname for Graham. Based on the spelling I would assume that 'Gray' would be the """correct""" spelling, but I guess that comes down to which of the two you were already using.