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Some words in philosophy are usually represented as theory of x. For example, logic is the theory of reasoning, epistemology is the theory of knowledge, ontology is the theory of existence, etc.
On the other hand, we sometimes consider the notion of existence and essence. I just wonder that do we have a "theory of x" representation for essence too?
Ontology is not "theory of existence". It is the study of Being.
Depending on the ontological paradigm, existence may or may not be equivalent to Being.
The dichotomy of existence and essence is an ontological concern, and can be considered to be a part of ontology.
Regarding Joseph's answer: Metaphysics is a very general term. Ontology can be considered a branch of metaphysics. It is inappropriate to consider metaphysics the "theory of essence", outside of a very qualified contextual usage.
Metaphysics might feasibly be presented as incorporating a formal study of essence and accident. However, metaphysics is much broader than just asking about essences. I guess what I'm trying to express is that arguments and theories involving essences should probably be classified within the category of metaphysics (though of course these questions do not exhaust its range of inquiry.)
In passing, a good starting point on the question of essence, at least in ancient philosophy, might be to look at Aristotle's Metaphysics; in particular, note that what in the standard translation is rendered as essence is in fact the curious phrase "what it was to be".
Also Theosophy (the first to write about the topic: Helena Blavatsky (1831–1891)), a philosophy which tries to know what can be known about the beyond physical.
