Would "chalcide" be understood as a group 16 dianion (and something less electronegative)? Would "pnictide" be understood as a group 15 trianion (and something less electronegative)?
From what I could find in a brief search, "pnictide"(this link includes some of the origin for the name) is used, but the corresponding term used for group 16 seems to be "chalcogenide", which, while it can be used to describe all group 16 elements, typically is used in a way that excludes oxides.
Pnictogens and chalcogens are the trivial names for group 15 and 16 elements respectively. From here:
Pnictogens – The elements of group 15: N, P, As, Sb, Bi. (Mc had not yet been named when the 2005 IUPAC Red Book was published, and its chemical properties are not yet experimentally known.)
Chalcogens – The elements of group 16: O, S, Se, Te, Po. (Lv had not yet been named when the 2005 IUPAC Red Book was published, and its chemical properties are not yet experimentally known.)
So, the corresponding ion names should be pnictide(e.g. nitride, bismuthide) and chalocogenide(e.g. sulfide, selenide, telluride). Note: salts containing oxygen as anion are called oxide salts but salts containing sulfur, selenium as anion are called chalcogenide salts. Since, salts containing oxygen as anion are more common and thus separately given name 'oxide salts' and salts containing sulfur, selenium as anion are less common, so they are collectively given name 'chalcogenide salts'.
Similarly, the trivial name for group 14 elements is crystallogens (for its ability to form crystals?) and for group 13 elements is icosagens or triels. However, these names are very trivial and rarely used.
I have never heard name of group 13 and 14 element ion as crystallogenide or icosagenide. Perhaps, for their inability/difficulty to form corresponding ions(since it is very hard to accept four or five electrons to form ions).