My advice is stop avoiding. Work on slowly becoming ok feeling shame (aka feeling like shit) and it will lessen. Then instead of avoiding you feel scared and shitty stuttering, you'll just stutter on your name, feel shitty, but a little less shitty and also a little proud that you didn't avoid or hide as much as you used to. Keep this up and eventually the shame will be less and less and stuttering will be less and less shitty.