Ever since I first read Lewis Ayres' groundbreaking Nicaea and its Legacy I have acquired a hobby horse about how there were no Arians after Arius. Well, strictly speaking that isn't true, there were some Arians, but the label "Arian" does not legitimately apply to 98% of the people it gets used for. So-called Arians didn't really follow Arius or his doctrines. Similarly most Nestorians, and the whole "Nestorian" church did not follow Nestorius. In fact, we now believe that Nestorius himself wasn't even "Nestorian" in his thinking.
Having spent not one, but two lessons talking about Chalcedonian Christology and the aftermath of that council (how many versions of Alexandrian miaphysitism can there be?) in a foreign language, I am more convinced than ever that we should stop labelling historical positions based on their founders, especially where that is not historically accurate. It's sometimes presentism and its sometimes reading history with glasses heavily tinted by systematics, but it's rarely good history.
So, for some examples:
"Arians" are better off labelled as "non-Nicenes", and depending on affiliation, "Homoiousian", "Homoian", "Heteroousian or Anomoian". For the most part, the Germanic migratory groups (Goths, Vandals, Lombards, etc..) can be labelled "Homoian" or simply non-Nicene.
The Nestorian Church is better labelled "Church of the East". This should not be confused with the "Oriental Orthodox", who in turn should not be confused with the Orthodox Church. Oriental Orthodox churches have followed a historic miaphysite position, and miaphysite is preferable to "monophysite", and to the ungrammatical "henophysite". Both macro-groups can be called non-Chalcedonian for convenience.
Let's also retire "Sabellianism" in favour of Modalistic Monarchianism.
Other important re-namings are welcome in the comments.