This is a common issue for stutterers. I used to get so anxious at meetings where I knew the introduction was coming that I’d nearly have a panic attack. A speech therapist could give you some strategies specific to your name - I think it would be so soften the M by relaxing your lips and adding more air. I get by sometimes saying “My name’s …” and getting a sort of running start into it. You can also just stutter and take a second to get it out. That’s OK!