When the thing you want to say is linked to a lot of emotion it can cause you trouble in saying it because your speech rhythm will tend to be messed uo due to the pressure the situation bestows upon you. Try to breath deep before saying your name. You can do this. Also, you need to expose yourself to saying your name often for this to get better as you need to reduce the instant panic that will rush through your body which might occur in the stressful situation.