What is the outer metal/plastic box of a device called?
Solution 1:
The cases for desktop computers are often called "towers". Cabinets house larger computers.
The generic name is "cases" from what I have seen.
https://www.computercaselab.com/knowing-the-different-types-of-computer-cases/
This site distinguishes between various types of "towers".
Solution 2:
Case and Chassis are used pretty often as some of the comments indicate. Other similar words are tower, system unit and cabinet. Also, holder is often used for additional external casing especially on smaller devices like smartphones and tablets.