Can't even say my name without stuttering

Can't even say my name without stuttering I'm nearly 35 and my whole life I've had a stutter since the age of 5. I've always struggled to be social as im always scared to introduce myself, leading me to lead quite an introvert life. As soon as someone asks my name I start to stutter as I struggle with pronouncing the 's' sound, which unfortunately is the letter my name begins with. My breathing becomes erratic and I can't seem to catch my breath. The person on the receiving side of the conversation always gives me a weird look. Either sympathy or thinking I'm a total weirdo. The worst one was when I went to a hospital appointment and the receptionist asked for my name. I gave her the appointment letter but she repeated she wanted to know my name. I couldn't get my words out and she rudely said 'I know its early, but its not that early that you've forgotten your name now is it.' I was so embarrassed and felt the lowest of lows. Having a stutter is such a curse. Everyday is like a burden just interacting with others. I hesitate to even make bookings to afternoon tea or days out as when they ask for my name I just can't say it without taking my time and stumbling on my words. The embarrassment of this just takes the whole fun out of it all. Any advice would be appreciated. TIA