Mathematically speaking, the term you are looking for is "Total Function" (a function that is defined for every possible value in some domain), as opposed to a "partial function", which is only defined for a subset of the possible input values.
Note that, strictly speaking, mathematical functions are always total on their own domain; calling a function "partial" only makes sense if you offset it against another domain, such as the function
f(x) = 1/x: the domain of this function is the domain of all real numbers except zero, but against the domain of all real numbers (including zero), it is partial.
In programming, the types of a function's inputs state a domain already, and by not defining the function for all of them, you could say that the function is partial. However, many programming languages fall back to a default behavior when you don't explicitly return anything - they may return 0,
undefined, etc. Technically speaking, such functions are still total - they return a value for all possible inputs -, but conceptually, there are gaps in the definition. And not all programming languages feature such fallbacks; the alternatives are refusing to compile, responding with "undefined behavior", raising an exception, etc.
BTW, note that neither determinism nor purity have anything to do with this. A deterministic function is one that always has the same effect given the same context (relevant system state and inputs); a pure function is a function that does not have any side effects (so that it always returns the same value given the same inputs, regardless of any outside state, and without influencing outside state in any way). You can easily come up with a function that is partial, yet fully deterministic (provided that partial functions are legal in your programming language, and definition gaps are handled in a predicatable way); and conversely, if you manage to write a non-deterministic function, e.g. by reading from a hardware entropy source, there is no reason why it would have to be total (nor partial). The same goes for purity, unless a definition gap automatically introduces side effects (then all pure functions must also be total).