Approach differently. Try switching up the way you introduce yourself. Instead of saying "my name is," you could opt for saying your last name first, followed by your full name. Additionally, you can begin your sentence in a unique way, such as using the phrase "the name is" instead of "my name is". Another method is to try speaking in different tones/accent. So if I were to ask you to imitate a British accent, would you stutter? For me, I won't. And this realization helped me change my voice just a bit to get on with the sentence. I'll make my voice higher or lower, speak slower or faster, make my tone more charismatic. It's quite simple, but it really helps the mental game.