You guys who are engaged in technology don’t need to think of fancy names. The main development direction is whatever it is called.
Personally, I think the development direction your department is more suitable for should be the supply of equipment for cloud and big data processing. It can be called "Cloud Computing and Big Data Basic Hardware Division". If it is not engaged in equipment, remove that one. "Basic Hardware". Whatever you say, the key is to fit in with your business scope.