People think I'm faking my stutter

People think I'm faking my stutter Earlier today in class I got asked how to pronounce my name, anyway, my name begins with a letter I usually struggle on, and I ended up stuttering on it. I felt really embarrassed after that, and these girls who were rolling their eyes claiming that I'm faking it for attention didn't help much either. If I was faking instead of really having it, I wouldn't be self conscious, nor would it look like I'm struggling saying my own name! I dont think I have to prove that it's real, if they think I'm faking it then I guess they're just ignorant or something, but, now I'm anxious about how people really see me. Do they see me as me, or as someone who fakes things for attention?