Is the expression "Deputy Head of Research" correct?
"Deputy Head of Research" is someone who deputises for the "Head of Research".

By contrast, "Deputy Head for Research" (or, sometimes, "Deputy Head (Research)") is someone who deputises for some generic "Head" in the specific area of research.

"Research Deputy Head" is unidiomatic and sounds like a command "go and research the deputy head" rather than a title. The "research" coming first somehow stresses it as a verb rather than a noun.

Even more common than any of those constructions, at least in my part of the world, is the simpler "Head of Research".

In practice, there will be a definitive answer to this question which you can only find out by asking within your university.