I could be wrong, but it sounds like ontology is the study of what things exist. But I wonder what is the name for the study of what changes happen? The study of action, change, motion, etc.
There is no accepted term for the study of change in metaphysics, analogous to ontology for the study of what there is, or mereology for the study of the parthood relation. Many scholars resort to the phrase "the problem of change", or "the problem of persistence".
I'm going to use the term metaphysics because while ontology is used as a synonym, some distinguish the former from the latter quite sharply (something along the lines of the study of being itself vs. mere conceptual analysis). Your distinction between change and being is a bit of a false one, I think, and you yourself propose the study of change, of something as if it were a something on its own without reference to anything else. The answer is metaphysics by virtue of the fact that change occurs in beings.
Historically, there was a debate between Parmenides and Heraclitus about exactly being and change; the former concluded that only being exists (think Zeno and his proofs of the non-existence of motion, otherwise known as change) while the latter concluded that only change exists ("you can't step in the same river twice", leaving the world essentially unintelligible). The former flies in the face of our experience: things do change. On the other hand, the latter is absurd if we admit the existence of things at all: it's not that you can't step in the same river twice, Heraclitus, it's that you can't step in the same river once, because even while you take your step, the river changes...as does your foot.
Aristotle's solution, which sought to reconcile being with change, was to define change, briefly, as the transition from potency to act and act to potency. So while the river changes, as does your foot, it is the river that changes, and it is your foot that changes. The change is only accidental, and not substantial, in this case. Changes in substance are still changes in something.
I think the question is clear. I don't think that there is such a term. The lack of a term, may show that the predominant tendency (within Western Euopean metaphysics) is to take impermenance/change as illusory, so needs not be blessed with a name, and 'Being' is more primary, is more real so its study is thus baptised Ontology.
It seems obvious that the question of impermanance/change does not then go away, but becomes subsumed within that of Being/Ontology.
A term for impermance/change seems to be a very useful thing; I suspect such a term could be imported from the Buddhist tradition where such a study is taken to be primary as Being/Essence is Sunya (nothing).
this question i think is a bit vague. maybe a question in response would be can you cite an ontological position which neglects change .. To frame the question in Heidegger's terminology ontology is grounded in the question 'what is being?', and guided by the question 'what are beings?' - for Heidegger the answer to the first question is found through interrogation of the second , so in relation to your question the fact that beings cannot escape change means it's impossible not to consider it in relation to Being, thus it's a neccesary thing to 'study' in the question of ontology.
There are many formulations of the nature of change within ontological prilosophy, Spinoza for eg.'s notion of conatus, that entities strive to preserve themselves within their present mode by avoiding entering into relations with their environment which tend towards decomposition, or Nietzsche who says the will to power in every entity forces it to reach always beyond what it is in order to overcome it's present mode of being and become stronger, more powerful .. i think there are innumerable examples showing how the study of change is included within the nature of ontological investigation.