When i first had to face my fear of stuttering, there was no substituting my name anymore (I actually have a nickname because my real name is a long one from another country ans fhe nickname stuck with me but I stuttered on that too) so there's no choice but to stutter through it.  I'd try to do a lighter touch more often than not with repeating it a couple of times seeing if it will come out on its own at first but it was more like a don't think, just do mentality.  Eventually it did become easier and eventually it became as easy as any other random word like talking with the wind but it took a lot of times of don't think, just do, and don't care.