What is the correct or different name for the radiator fan control relay?

It's a very fairly easy component that goes wrong, However, you may - or - may not find the answer on Google....Just go into your local auto store, and they will help you....

The SAE Society of Automotive Engineers.. has created a common (accepted) terminology that applies to all manufactures... Automobile parts to avoid confusion when communicating, BUT most people have no clue, of the SAE so you will hear many terms for the same component. Example they term the Computers that regulate engine management, fuel maps and ignition timing, and other minor functions. PCMs but here few other "names" ECU, EEC, PEM..on and on.

It's commonly called a fan control module