The parshah in Vayikra Chs. 16-18 is often called "Acharei Mos", but sometimes the "Mos" is omitted. Is either version of the name more correct than the other, or did is it minhag-dependent (Ashkenazi vs. Sefardi?), or did one become more common over time? If so, why?
It is certainly minhag dependent, but not necessarily Ashkenazi and Sefardi dependent, rather it may fall along different lines. Within Ashkenazim you will see it both ways.
The Lubavitcher Rebbe says (Likkutei Sichos 5 p. 57 second paragraph of note 2) that from Rashi on Sota 40b it seems that Achrei Mos is the name of the sedra, so Rashi needs to clarify that the mishna is referring to only the first parsha of the sedra (whereas in Megillah 30b since it follows "Parshas Moados" it is clear that it is only referring to the first Parsha).
So we can infer from Rashi that the sedra was Achrei Mos in his time, and that the Mishna is refering to those words as the first of the section, using both words, not just Achrei.
Pure speculation: Some name Metzorah as Tahara, to use a nice language. It could be the Mos (meaning death) was dropped from the name of this Sedra in order to avoid using a negative word.