I can't speak to the specifics of the Soviet Union, but I want to address the opening assumption of the question.
Generally, Communism believed in economic central planning, with each field being serviced by one "company" (to avoid waste).
This is untrue of (or at least unnecessary for) both communism and centrally planned economies. A centrally planned economy is one where production, prices, and distribution are set by the government, not by market forces. No monopoly is necessary. Communism does not require a centrally planned economy, but rather is about the ownership of the means of production which covers a wide spectrum of social, political, and economic structures.
What you're asking about is the Soviet model. It's important to not use the Soviet model as a stand in for communism. Communism is a very broad set of social, political, and economic philosophies. The Soviet model is a specific, and rather broken, flavor featuring a centrally planned economy, single party control, and powerful committees. The Soviet model is more like an oligarchy masquerading as communism.
Two examples of centrally planned economies within the United States are large scale manufacturing for the military and, until very recently, space. The US government is the major buyer of things like aircraft carriers, tanks, nuclear submarines, and heavy launch vehicles. They effectively control what is produced, who it gets distributed to and, somewhat, the price.
The US government deliberately doles out contracts to multiple suppliers, even to the point of paying more money, in order to keep multiple suppliers around (also to get the votes of powerful senators by funneling money to their districts). This is to foster competition, prevent a single company from controlling the market, and also as a hedge in case one goes out of business.
For example, there were two builders of US Navy submarines, Newport News Shipbuilding and General Dyanamics Electric Boat, but reductions in the US navy's submarine fleet means now there is only one, Electric Boat. Should something happen to General Dynamics this would be put the US's ability to build submarines, a highly specialized skill, in danger.