I can't saying my name without lisping, stammering and mispronouncing. Help!

I can't saying my name without lisping, stammering and mispronouncing. Help! I used to be a heavy stutter as a child and had a bad lisp. My stutter faded as I got older and has been gone for years now. My lisp was a bit more of challenge but eventually it was not an issue anymore and I could speak to anyone without sounding like I have lisp anymore. It's not something I even think about anymore. I have one issue though. Whenever I need to introduce myself to people, I quickly feel myself tense up with anxiety and mispronounce my name. I mess up the s and r sound in my name that I have to repeat my name to people. This only ONLY happens on my name and no other word. I literally fumble my name drastically, I also feel a block before saying my name and many times have to 'uuuhhh' before saying my name. It feels like anxiety and a psychological thing because of how I was teased for it in the past.I just want to be able to say my name like any other word I am able to say on any day. I can say my name easily and clearly in a room alone, or to my family, but when it comes to meeting new people, it's a problem. Please help.