The generic name is the chemical name of a medicine. This name is the same no matter how many companies manufacture the medicine.
When a company makes a medicine, they give it a brand name (or trade name). A generic name medicine can be made by more than one company. And each company may have their own brand name for the same generic name medicine. So there can be more than one brand name for each generic name. Generic names and brand names of medicines are chemically the same. But generic name medicines are usually less expensive. A doctor may be able to prescribe a generic name medicine if it is available and appropriate.