I don't think it was Pearson who coined the name. Wikipedia dates it back to 1875, when Pearson was 18. Its more likely (to me), that its use grew organically, and is associated with Pearson because of his influence.

> this is not accounted for by assuming a normal distribution

Often, groups with different averages produce a normal distribution when combined. So it may be the right distribution, but not the proper conclusion.