[MarkusQ]

If we're talking "proper math terms", if it "returns a random number" it isn't a function. In math, the value of a function can't change unless the arguments change. If you evaluate it repeatedly with the same argument(s) you'll always get the same result.

[dahart]

Yes, you’re right, good point. Maybe there is no one good term for this case (but given the ocean of terminology, I’d be slightly surprised). ‘Not a function’ also isn’t the right term here because functions of x that returns a constant are okay - they just don’t depend on x. Hashed random functions are true functions but are designed to be non-invertible, so maybe non-invertible (or irreversible) is a decent single term for what @vunderba meant. Other terms that broach it might be ‘non-injective’ and ‘entropy-reducing transform’. I suspect those aren’t technically strong enough for the kind of information loss we need in this context.