What is the medical term for a hernia containing fat?

The medical term for a hernia containing fat is a "lipoma." However, if you are specifically referring to a hernia that involves fatty tissue protruding through a weakness in the abdominal wall, it might be called an "inguinal hernia" or "ventral hernia" depending on the location. These hernias can contain various types of tissue, including fat, and may require surgical evaluation.