I’m sorry you’re having to go through this. It hurts no matter how many times it happens. Ultimately you want to get to the point where it’s not nagging at you afterwards about what happened and isn’t affecting your daily life. Caring less about it is probably what would help you stutter less but it’s easier said than done. But what can help temporarily is putting a word or phrase before the name like “uh” or “my name is.” Or speaking in a different tone or loudness level. This doesn’t always work and your mind can become accustomed to these crutches. All it takes is stuttering on these crutches and then your mind becomes anxious around them as well. Ultimately, people care, judge, and think about it in the moment, but it doesn’t take long for them to move on with their preoccupied lives. We put too much emphasis on what people think about us.