name for stereo system in single case


A few current product designs feature stereo driver pairings in a single unit, essentially offering the simplicity of radio boxes, but playing an external audio source.

Many are extremely inexpensive designs packed with high-tech features, but a few are more subdued, extending the low-end of the range of mid-range manufacturers.
A few examples of the following:

The aim of course is not to satisfy the most discerning audiophile, but to make a pleasant experience with very modest demands on space and investment (for example, in a kitchen, someone listening frequently to talk but occasionally to music).

Is any particular name given for such a product, that is, one essentially having the following features?:
  • A single case
  • Stereo speakers (drivers, e.g. two woofers and two tweeters)
  • Internal amplification, for line input to the whole unit.
thinker
Naim has a rather expensive line of products often referred to as "all in one" systems. You still need to add speakers to them.  The "all in one" label seems to fit the OP's scenario just as well.
HA...I had one of those "boom boxes" tied to the head of my rack onboard ship when I was in the Canadian Nsvy back in 81, used headphones mainly or took it up on the helo flight deck at sea. It was a single cassette deck with am/fm "stereo" tuner. It had huge dual 8" speakers with "base boost" feature by Sony and took 10 D cell batteries if I recall correctly. 
Hah! It’s only a boom box if it has a handle on top. Gotta carry it on your shoulder or hanging down below, walkin’ down the getto while blasting Easy E!

https://www.youtube.com/watch?v=IwOEDNGW5mA

As far as the OP is concerned, I think these are really just called "bluetooth speakers" nowadays. I thought you were going to mention something like this:

https://www.bestbuy.com/site/yamaha-micro-component-system-white/4723607.p?skuId=4723607

It looks like Best Buy is calling these "Stereo Shelf Systems".