It can be a sole proprietorship enterprise, and its name can be: xx family farm in xx county or Xx planting family farm in XX county.
Can be a partnership, the name can be: xx family farm in xx county (limited partnership, general partnership) or xx planting family farm in xx county.
It can be a company, and its name can be: xx County xx Family Farm Co., Ltd. or xx County xx Planting Family Farm Co., Ltd.