Should I always refer to it as "the empirical study of/ involved in this thesis"? I found it too lengthy when I need to refer to it frequently in the thesis. Is there another shorter term to refer to it?
If there is no ambiguity, "The Study" should do after the first instance. You could even say, at the first usage
...the empirical study of this thesis (The Study)...
This would make it a sort of keyword for the remainder of the thesis.
If there might be ambiguity, then The Present Study would probably be enough to clarify.