Is it acceptable to refer to theories to support an argument? In my field, education, there are many named theories, for e.g., the “Atkinson-Shiffrin memory model”, which educators often talk about and debate.

While writing various graduate papers, my professors have often asked me to cite various named theories to support my arguments. Can theories generally be used to support arguments? Are theories more than just names for ideas? Can any person coin a new theory, or is there some process by which a theory gains recognition and support before it is deemed a “theory”? Can I really cite theories to add support to my papers?
Are theories more than just names for ideas? 


No, they are just names for ideas.


  Can any person coin a new theory, or is there some process by which a theory gains recognition and support before it is deemed a “theory”? 


Anyone can coin a new theory, and the term “theory” does not imply any special status.  For example, the flat earth theory is a theory, just not a good theory.  As a general rule, people don't spend much time talking about theories unless they are valuable or controversial.  If you make up a new theory without some real insight, probably everyone will just ignore it.  But that doesn't mean it's not a theory - it's just not a useful or interesting theory.


  Can I really cite theories to add support to my papers?


Part of the point of citing these theories is to show how your work fits into the field.  You are engaging with and responding to certain ideas, refining or extending some of them and correcting or refuting others.  It's important to describe these ideas in a recognizable way, so readers will see the context for your work and can better understand what you mean.  Sometimes the best way to do that involves referring to named theories.  If you can explain how these theories help justify your conclusions, then that will add support for your ideas.  (You're taking advantage of the fact that many experts already understand and agree with these theories.)

Another factor that may be relevant in graduate papers is proving that you understand these theories and can explain how your work is related to them.


  While writing various graduate papers, my professors have often asked me to cite various named theories to support my arguments.


I'd strongly recommend discussing this with them.  People on the internet can offer general comments, but only your professors can tell you exactly what they are looking for and why.