What would be a good term for a 'randomness generator' if that term is not suitable?

Fun question. The problem is, algorithms, programs and systems can be designed to generate specific things AT random, but not to generate randomness itself as an abstract construct. An algorithm that generates numbers at random, such as those used for lotteries, is a random number generator. You can also have random word generators as you mentioned, random scenario generators, and so forth. However, they all generate specific concrete things or categories of things, not randomness itself. The only example of something that comes close to generating randomness is the Hitchhiker’s Guide to the Galaxy's “Heart of Gold” vessel powered by an Infinity Improbability Drive: it can produce a whale, a pot of petunias, etc. Even then, it’s generating random things, not randomness. That would be like generating chaos or goodwill. It’s a fascinating idea for a sci-fi novel, but I don’t think it would have any real-world applications. As such, I don’t think the word you’re looking for exists.

I'd call such a device an entropifier.

I'd be sort for entropic modifier of course. You can even look it up:
http://forums.philosophyforums.com/threads/the-metaphysics-of-the-nervous-system-70632-22.html

Anyway it sounds much better than an entropygator (...yes, an entropy generator).

Randomizer is commonly used for this sort of device. https://www.random.org/lists/ is one example, but google gives over 200k hits for the term.

Chaos
The apparent absence of form. Lexico gives:

Complete disorder and confusion
Or:
Physics The property of a complex system whose behaviour is so unpredictable as to appear random, owing to great sensitivity to small changes in conditions.

A Wikipedia article says in part:

(Ancient Greek: χάος, romanized: kháos) refers to the void state preceding the creation of the universe or cosmos in the Greek creation myths, or to the initial "gap" created by the original separation of heaven and earth. --Wikipedia

However, I must emphasize that the absence of form in this "unprogrammed" Universe is apparent, not true absence. Nothing comes from nothing, you know. For this reason, Chaos is sometimes defined as "sensitive dependence on initial conditions". A butterfly flapping it's wings has an effect (uncalculated at the time) on a windstorm halfway around the globe. This hitherto uncalculable effect means basically that the only way to find out what will happen is to do something; and once that is done, you can never really know what might have happened if you haden't. However, it can be argued that true randomness is a chimera, a mirage. Just ask any programmer trying to generate it.

The mathematical phenomenon of chaos is studied in sciences as diverse as astronomy, meteorology, population biology, economics and social psychology. While there are few (if any) causal mechanisms such diverse disciplines have in common, the phenomenological behavior of chaos—e.g., sensitivity to the tiniest changes in initial conditions or seemingly random and unpredictable behavior that nevertheless follows precise rules—appears in many of the models in these disciplines. Observing similar chaotic behavior in such diverse fields certainly presents a challenge to our understanding of chaos as a phenomenon. --Stanford encyclopedia of philosophy

"Chaos" has been studied by mathemeticians, but it is, in the end, beyond mathematics. It represents the "universal random seed generator" that no-one has ever been able to predict. As an article at Euronews says:

You can think about flipping a coin. In that case, you flip a coin and the result is random, but the reality is that the randomness of this coin is not intrinsic to the coin, it's our inability to predict its dynamics. In reality, the process is predictable.

Wired gives a more developed exposition:

Which is why, a couple years ago, Bierhorst’s team decided to develop a number generator that was perfectly, provably random. In the cryptography world, that means “numbers that cannot be predicted,” says Ribordy. And what’s random? Quantum mechanics.
It’s like this: Even if you repeat a quantum experiment by preparing a quantum particle in exactly the same initial state, subjecting it to the exact same conditions, measuring its orientation after the same amount of time, you can still end up with totally different results. This is unlike flipping a quarter, where its initial conditions—the force of your thumb, the direction of the winds—determine the outcome before it lands. The outcome of “flipping” a tiny quantum particle only exists as probabilities until the moment it “lands.” Electrons, photons, and atoms are really, actually random.