The first rule of improv comedy is, “don’t deny.”1 If your partner says something about you, it’s true; if you don’t like it, work around it. If you stop and say, “No, I’m not a beet farmer, I’m a rocket scientist,” then the scene loses all interest for the audience and becomes two annoying actors squabbling.
I hereby arbitrarily assert by the authority vested in me as a guy with a blog, this rule applies equally to introductions to academic talks. If someone mispronounces your name, let it go. If they get the title of your book wrong, you can if you really must find a way to mention it properly yourself, without explicitly correcting your host. If they say you’re an expert in x and that’s why you’re giving this talk, and it turns out your talk isn’t really about x, you can probably find a way to say, “Yes, I have interests in x, and those led me naturally to the material in this talk.”
Obviously, this whole post falls under the heading of dicta or at best free advice, and maybe there are outlying cases where it’s really necessary to correct the introduction, but seriously: it’s jarring to the audience if you spend the first few minutes of your talk explaining that the apparently gracious introduction you just received is all wrong and that really your theoretical inheritance is a bit different from what they heard in the lead-in.
1Also, I should mention, I’m not very good at improv comedy. I just remember the rules.