How to address title-field inconsistency?
Your Ph.D. is in the department is says it is in, and there's nothing that you can (or should) do about it.  For example, my Ph.D. is in Electrical Engineering and Computer Science, but my thesis didn't really have anything to do with EE.  That's OK: most people understand that the actual names and structures of departments are complex and often historical artifacts.

What will really speak for you in your application is your thesis and publications.  If the titles of those clearly show your area of work, then just make sure that they appear clearly and prominently wherever you present yourself.