If one looks at the roots of science, it is not founded on being right, but on being easy to prove wrong. Popper's concept of falsification puts this in words.
No fact, or finite set of facts, can prove a scientific theory, or any other kind of theory. It is possible for a fact to contradict a scientific theory. This isn't the same as it being easy to prove a theory wrong. You have to find a consequence of the theory that could be tested, and set up a situation in which this consequence could arise. At every step, you have to make guesses and your guesses could be wrong. You may have a revisit many of your guesses and try to come up with better ideas. All knowledge, scientific or otherwise, is guesswork controlled by criticism. See Is everything just an opinion?.
I see many who see the absence of falsification of a theory and make the fallacious assumption that that is proof that that theory is right. I know the general fallacy of "absence of evidence is not evidence of absence." However, in the modern era, I am finding this fallacy occurring more and more often with regard to scientific theories. Theories are deemed "proven" because of lack of evidence to the contrary. This can cause great consternation when the theory is later proven false and a new model put in place. We have to explain why a "proven" concept is suddenly now wrong, when it was not wrong yesterday. It is often latched onto by those who approach the world with alternate viewpoints to cry "See! All of science is false!"
Scientific knowledge is not proven, nor is any other kind of knowledge. Popper was explicit on this point, see "Realism and the Aim of Science", Chapter I. People who want to claim that some theory or another is proven are just trying to duck responsibility for making their own judgements, and for persuading critics through argument.
Those who claim that the correction of an error is some sort of indication that science is broken are silly. Would they prefer a means of discovering knowledge that never corrects errors? Or do they imagine that they have access to an infallible oracle?
Given that this is a major issue to be address in the philosophy of science, I'm wondering if there is a word which is given to this fallacy explicitly with respect to the falsifiability of scientific theories. It is not uncommon for special instances of a general pattern to be given a name to facilitate communication. I'm wondering if this may have already happened here, so that I can use the best terminology I can.
I don't see that it makes much difference what words you use to describe the mistakes I explained above. The people who make such mistakes don't understand the arguments involved. Until they understand the arguments terminology won't help them understand, and it may give people a false impression that they know something they don't properly understand.
Having said that people who think science proves stuff and those who crow when a scientific theory is refuted are usually both making a mistake Popper called "justificationism": thinking that it is possible and desirable to show that positions are true or probably true. It's very rare for people to understand even this point, so my guess is that you won't need much more terminology and if you do, make it up as you go.