Sending a card, signing it 'Nathan' or not, suggests you still want to have a decent relationship with your father and aren't ready to resign yourself and him to be another case of estrangement. I think you should send one, since its a little effort that could go a long way in the long term. Yes, it might vex him a little to begin with should you sign it with your REAL name, but I think eventually, whether it by his own mind or not, he should hopefully be able to overlook that and take to heart that you still want him in your life whatever happens.
Hope that made sense. xD