Advice on coping with a speech impediment...?

If most people get embarrassed when they realize the situation then it doesn't seem they are unkind and if they are not unkind you may just want to explain the situation first. I realize that may seem a bit weird but maybe you can try it and see if you feel less embarrassed by explaining the situation instead of having to repeat yourself. That would be if you know someone a little bit. If you're just introducing yourself to someone for the first time ("Hello my name is...") maybe you could just give them your first name.