We say: graph theory , group theory, number theory , set theory, what is definition of theory?
We also say abstract algebra, real analysis, but why we do not say abstract algebra theory or real analysis theory? What is meaning of theory?
We say: graph theory , group theory, number theory , set theory, what is definition of theory?
We also say abstract algebra, real analysis, but why we do not say abstract algebra theory or real analysis theory? What is meaning of theory?
The names you listed in the first paragraph are built from an object of investigation. You study objects named X and prove a bunch of things about them, so you call it X theory.
So, it's "group theory" because it concerns the properties of groups.
We would not say "real analysis theory" because "real analysis" is not a name of the object under investigation. We are not proving theorems about some properties of real analysis. But it could be called "real function theory", which is indeed a term in use, albeit not as common as "real analysis".
"Complex analysis" vs "Complex function theory" is close enough so that Wikipedia acknowledges both.
Whether one or the other name becomes more widespread is influenced by many things, including the personal preferences of people who were particularly influential when the theory was in formative stages.