name for stereo system in single case

Mini-Console?

It's called the Bose Wave.

We have a Klipsch The One II at our mountain condo. It is great for filling small spaces. I'd highly recommend it.

Oz

"...name for stereo system in single case..."

Bluetooth speaker?

Back in the day they were called a “compact stereo system”

“Arthur”.

I had Magico build me one. All in one stereo, fills the room with sound, very high quality. Only 3x7x15 (feet), and at 3 tons requires a forklift. We call it, "Tiny Tim".

Junk on a budget.

Back in the 70’s and 80’s, a stereo system in a single case was called a "Boom Box" Some of them were so big they made Mr. T look like Urkel.

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.

Highly Intergrated Stereo System?

aka...HISS

Limited Output Wireless Fixture?

aka...Low-Fi

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".

As far as the OP is concerned, I think these are really just called "bluetooth speakers" nowadays.

In practical terms, I agree in a large sense, but Bluetooth is an input, not a cabinet design or driver layout. I was genuinely curious whether this physical configuration had any particular name, since it of course in principle can be constructed without any Bluetooth receiver.

By the way, a web search with key words "bluetooth speakers" mostly produces products in two categories, one being a genuine stereo speaker pair with a Bluetooth input, the other being a small battery-powered device, very much as a modern-day boom box, of very low cost and basic construction, suitable for outdoor recreation, and the like. Neither of these two broad categories quite encompass the description I gave. Hence, I think, a new name is badly needed.

Of course many, especially in this community, would have limited interest in such a configuration, but in my view it may not be as frivolous as some might assume. Once getting passed the idea that not every room in the world is as meticulously arranged as an audiophile’s living room (I know, it’s hard), and thinking about spaces like kitchens, hallways, and bedrooms, where a transistor radio would have been common in yesteryear, I think that some would start to see the usefulness. I think many are still unaware that an appliance as small as 50 centimeters long, smaller than a mobile phone, in fact essentially a phone with no screen or battery, can easily provide the audio source, connecting to a local media server or internet radio channel. Functionally, the effect is the look of a mid-century radio box combined with the ability to play an uncounted variety of of live or recorded sources.

As I said earlier, they were called compact stereo systems where the receiver had a turntable built in on top and the front face had either a CD player/recorder or an 8 track tape player.  I sold dozens of them during the 1973 Christmas season.  Sony actually made quite a nice sounding unit for around $200.00. KLH also made one that sounded pretty good for the money.  

A system of the turntable, tape deck, or CD tray integrated, versus a cabinet of just the drivers, amplifier (and DAC) is a big difference. Wouldn't you say that the "compact system" designation is likely to apply only to the fully integrated case?