The name of the process where an object is exposed to nuclear radiation is called "irradiation." Irradiation refers specifically to exposing a material to ionizing radiation, but it does not make the object itself radioactive. This process is often used deliberately, such as sterilizing food or medical equipment by exposing them to gamma rays or other radiation types.

There is also a related concept called "induced radioactivity" or "activation," where a stable material is made radioactive by nuclear reactions involving neutron absorption or other particle interactions. But the general term for exposing an object to nuclear radiation is irradiation.