Step 1: Understanding the Concept:
The question asks for the more common name of the Ilbary dynasty, which ruled the Delhi Sultanate.
Step 2: Detailed Explanation:
The Mamluk Dynasty, which ruled the Delhi Sultanate from 1206 to 1290, is commonly known as the Slave Dynasty. The term "Ilbary dynasty" refers specifically to the lineage of Iltutmish, a prominent ruler of this dynasty who belonged to the Ilbary tribe of Turks. Since many early rulers of this dynasty, including its founder Qutb al-Din Aibak and Iltutmish himself, had origins as slaves (mamluks), the entire dynasty is popularly called the Slave Dynasty.
Step 3: Final Answer:
The Ilbary dynasty is famously known as The Slave Dynasty.