In most videogame engines I've worked with, it's called "screen shake" or "camera shake". In film it seems to be referred to as "handheld" for live action footage, and I can't find anything to suggest that in animation storyboarding they don't also just use the term "screen shake" or "camera shake"
Just because something is used in a professional context, doesn't mean it needs a complicated or pretentious. It's often easiest to use the term that most clearly describes the effect.
The term used for anime is probably just something like "shaking effect" or "shake screen" but in Japanese, honestly, or might even be "screen shake" in katakana, since tech terms are often English loanwords. It's kind of tricky to look up.