What do you call a professor that is hired by two different departments?
It's usually called a joint, secondary or courtesy appointment.  The purpose is to allow faculty to teach or do research in cross-disciplinary topics.  Someone with a joint appointment is usually a full member of both departments and funded by both; secondary and courtesy appointments reflect a looser relationship.

Their formal title will be a list of their appointments, e.g., "Professor, Electrical Engineering; Professor (courtesy), Applied Physics".

To an audience, they might be introduced as "Professor of Electrical Engineering and, by courtesy, of Applied Physics", but beyond that, there's no special term for someone who holds this type of appointment.  They're still just called a professor, same as the rest.