It will barely work at the top
As @AlexP put it quite well So you were thinking about the Soviet Union, an empire with one flag, one language, one bank (actually it had two, one for the Soviet slaves and one for reluctantly trading with the vile imperialists), one retail company, one Academy of Sciences, etc. etc., all lead by the One Secretary General of the One Politburo of the One and Only Party. As you know, it was a peaceful and prosperous empire, of which the subjects did not at all risk their lives to flee abroad, and which absolutely did not kill millions of its own people and certainly did not imprison many millions more at hard labor.
I don't normally quote long comments in an answer, but that one is well done and almost exactly what I was already thinking.
That being said, it did work, at least nominally, at the top of the stack. Hard to do "big science" under the table. The same goes for banking, mass transit and many other things. We even have this in many capitalist/democratic countries - e.g., there is often a single regional (or even national, depending on the size of the country and the particular industry):
- Postal Service
- Utilities - Water, Electricity, Natural Gas, Telephone
- Central Bank (though capitalist countries, by their nature, will normally have other banks at a lower level that actually deal with individuals and businesses)
- Mass Transit - many countries actually started with private railroads and eventually nationalized them to save them from bankruptcy (e.g., Amtrak).
Some things just naturally lend themselves to a monopoly or near-monopoly situation. Look at pictures of Manhattan at the beginning of electrification - lots of wires going all over the place because there was no central electric company, which was both inefficient and dangerous.
It will not work at all at the bottom
Look at any communist country. Whether sanctioned or not, capitalism happens. Typically the government eventually realizes it is a necessary evil and will sometimes even support it - look at China today. But even where it is not officially sanctioned by the government, at the small level there is almost ALWAYS capitalism.
If the monetary supply is too tightly controlled then people will resort to barter. I'll fix up your house if you give me 1/2 the eggs from your chickens. The government is counting the eggs? No problem - give the officer extra milk from your cow.
In a government as described, typically only the very top level lives really well. The lower levels tend to be open to corruption - bribes to "look the other way" and making deals to get what they need.
This can even allow you to work with some friends to build a bigger house. As long as the building inspector gets his "fee", the one-and-only construction company (including the CEO who gets a cut from the building inspector to supplement his meager state-determined salary) will look the other way too.
Even in a planet with just one nation, there will be a black market for forbidden (or very limited access) goods. Hard to suddenly come up with a luxury car when only the top government staff are supposed to have them. But a color TV in your house when you are only supposed to be able to afford black & white - no problem if you have friends in the one TV factory. The classic examples - cigarettes, alcohol, etc. are even easier as they are extremely portable.