I used to have to say my name on the phone at work and people would often say "are you SURE that's your name, ha ha!" (because I said it slow in a way that made it sound like I was just making it up on the spot). I would just say in a friendly way "actually no, I have a stutter. How can I help you?" I'm never going to "pass" as a person who doesn't stutter, so I might as well just mention it as a fact. Same as if somebody thought I had blue eyes and I said "actually no, I have brown eyes." There's nothing vindictive about mentioning an important fact about yourself and no reason not to mention it.