It's not just farms - the concept is known as a Cooperative, or Co-Op.
Collective
Right.
Yeoman
Yeomen
either state farms, consumer farms, corporate owned farms, or family owned farms
Hillshire Farms is owned by the Sara Lee Corporation
A group of shops all owned by one company is called a chain.
This system is often called "collectives". It was one of the prime goals of Vladamir Lenin.
Corporation
shareholders
Collective farms are a type of farm that are owned and operated as a joint enterprise by peasants. They are also known as communal farms.
A lot of the large companies that run farms are farms or ranches that are family owned: A company is just another business term for a group of people who operate a business, no matter if it's a farm, a ranch or a cosmetics-producing company. They are just called "companies," often with a name in front like "Blue Ridge Cattle Co." for instance.