I've always known these (at least in their single-valued incarnations) as argmin & argmax, and I've even seen them used with those names in mathematical literature. I would prefer a naming scheme where the "arg-" prefix indicates that we return the index/indices which induced the extremal value(s) (and not the extremal value(s) itself/themselves), and the "-ima" suffix indicates that we return multiple values when there is a tie.

It never occurred to me that a plural version of them might be useful, but I don't see why not. Perhaps the two optimized cases could even be combined efficiently by checking wantarray.

Whatever you want to call it, I'm with you in that I've always wanted functions like these included in List::Util.