Thankfully my name isn't really something I stutter on but I totally understand how bad it must feel. Stuttering in front of others in such cases is always extremely happy humiliating. Have you tried adding some sound before your name to help you start off? For me it usually helps to say "e" silently so it'd sound like e[my name]. People don't even notice it but it helps a ton. Obviously for you it can be some other sound, something you can say quite easily.