What is hereditary breast cancer called?

BRCA-1 & BRCA-2 gene. Hereditary mutations in either brca-1 or brca-2 genes predispose carriers to developing breast cancers usually at an early age. Other cancers like ovarian cancer can also occur commonly even in the same patient.
HBOC. Hboc=hereditary breast and ovarian cancer, which is due to a mutation in the brca1 or 2 gene. There are other inherited cancer syndromes that increase the risk of breast cancer. These include cowden's, li-fraumeni, lynch, peutz-jeghers, and hereditary diffuse gastric cancer syndrome. But 85% of breast cancer just happens, unrelated to any of these inherited syndromes.
No specific name. About 3% of the breast cancers are due to inherited anomalies. These are due to many different dna changes. The more commonly known breast cancer genes are brca 1 and brca 2.