> It's not because they're frothing at the mouth racists, it's because they're minorly inconsiderate.

There is a very good chance that your correction is coming off as inconsiderate since it is interrupting the flow of conversation and perhaps even the other person's train of thought. That interruption is also going to affect how well they remember the correction. If they were unprepared for an off-topic interjection, it is probable that they didn't hear what was being said or it did not register in their memory.

So yes, getting people's names correct is important. On the other hand, letting people get your name is important (rather than forcing the issue).