If this is really going to be a function (which I very much disagree should happen, but oh well), then IMO there's really only a single of logical name for what it should be:
func _ (arg1: Type1)
This is not a feature like subscript, because we've decided we're still going to have func as part of the signature, which is not the case when declaring a subscript-able type. Therefore, I don't think we need an additional special keyword-name.
What we're technically describing here is the ability to call a function on a type, but where that function does not have a name. In Swift, the syntax for "this is unnamed" is to use _. So having the callable function be func _ (...) is consistent with existing syntax, because it means "This is a function, but it has no name", which implies you'd call it by omitting the name, which means it is the "callable" function:
struct Adder {
let base: Int
func _ (adding value: Int) -> Int { return base + value }
}
let a = Adder(base: 40)
let answer = a(adding: 2) // calling a function with an omitted name